ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lew...ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lewy (CFL) coefficient. Toro and Titarev employed CCFL=0.95for their experiments. Nonetheless, we noted that the experiments conducted in this study with CCFL=0.95produced solutions exhibiting spurious oscillations, particularly in the high-order ADER-WAF schemes. The homogeneous one-dimensional (1D) non-linear Shallow Water Equations (SWEs) are the subject of these experiments, specifically the solution of the Riemann Problem (RP) associated with the SWEs. The investigation was conducted on four test problems to evaluate the ADER-WAF schemes of second, third, fourth, and fifth order of accuracy. Each test problem constitutes a RP characterized by different wave patterns in its solution. This research has two primary objectives. We begin by illustrating the procedure for implementing the ADER-WAF schemes for the SWEs, providing the required relations. Afterward, following comprehensive testing, we present the range for the CFL coefficient for each test that yields solutions with diminished or eliminated spurious oscillations.展开更多
Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under...Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.展开更多
International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper int...International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper integrates the existing research of international carbon tax scholars to the classification and comparative analysis of international carbon tax schemes.Using a literature review approach,this dissertation mainly applies the method of qualitative analysis to explain and compare the contents of four international carbon tax options.Through the analysis and evaluation of individual countries’carbon tax practice,the two-country model is verified.Through the method of comparative analysis,the schemes are evaluated from four dimensions and an assessment is made.The difference of carbon tax among countries makes the internal policies of countries adjust accordingly with the changes of international environment,which promotes the gradual convergence of carbon tax schemes.The results intend to provide reference to further study the issue on international carbon tax.展开更多
Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,c...Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.展开更多
Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do ...Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.展开更多
Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisi...Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.展开更多
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamicall...In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.展开更多
This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two...This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.展开更多
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.展开更多
A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can e...A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.展开更多
This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary ...This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.展开更多
In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the m...In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the main contributor to the stability of the slope.Then,two widening schemes are proposed,which are the steep slope with strong support and the gentle slope with general support schemes.The static/slope module of MIDAS GTS finite element analysis software and the strength reduction method were used to compare the two schemes.The results show that the steep slope with a strong support scheme has obvious advantages in land requisition,environmental protection,and safety and is more suitable for reconstructing and expanding the highway slope.展开更多
Mesh reflector antennas are widely used in space tasks owing to their light weight,high surface accuracy,and large folding ratio.They are stowed during launch and then fully deployed in orbit to form a mesh reflector ...Mesh reflector antennas are widely used in space tasks owing to their light weight,high surface accuracy,and large folding ratio.They are stowed during launch and then fully deployed in orbit to form a mesh reflector that transmits signals.Smooth deployment is essential for duty services;therefore,accurate and efficient dynamic modeling and analysis of the deployment process are essential.One major challenge is depicting time-varying resistance of the cable network and capturing the cable-truss coupling behavior during the deployment process.This paper proposes a general dynamic analysis methodology for cable-truss coupling.Considering the topological diversity and geometric nonlinearity,the cable network's equilibrium equation is derived,and an explicit expression of the time-varying tension of the boundary cables,which provides the main resistance in truss deployment,is obtained.The deployment dynamic model is established,which considers the coupling effect between the soft cables and deployable truss.The effects of the antenna's driving modes and parameters on the dynamic deployment performance were investigated.A scaled prototype was manufactured,and the deployment experiment was conducted to verify the accuracy of the proposed modeling method.The proposed methodology is suitable for general cable antennas with arbitrary topologies and parameters,providing theoretical guidance for the dynamic performance evaluation of antenna driving schemes.展开更多
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g...In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.展开更多
In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid colu...In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.展开更多
Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the...Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.展开更多
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is us...The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step size is chosen based on the size of the background cells.In May and Berger(J Sci Comput 71:919–943,2017),the mixed explicit-implicit approach in general and MUSCL-Trap(monotonic upwind scheme for conservation laws and trapezoidal scheme)in particular have been introduced to solve this problem by using implicit time stepping on the cut cells.Theoretical and numerical results have indicated that this might lead to a loss in accuracy when switching between the explicit and implicit time stepping.In this contribution,we examine this in more detail and will prove in one dimension that the specific combination MUSCL-Trap of an explicit second-order and an implicit second-order scheme results in a fully second-order mixed scheme.As this result is unlikely to hold in two dimensions,we also introduce two new versions of mixed explicit-implicit schemes based on exchanging the explicit scheme.We present numerical tests in two dimensions where we compare the new versions with the original MUSCL-Trap scheme.展开更多
In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,...In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,the mass conservation,mole balance and energy conservation are kept simultaneously while the positivity for the density and pressure is preserved unconditionally even with stiff reaction networks.It is proved that the first-order truncation terms for the Patankar coefficients must be zero to achieve a prior third order of accuracy for most cases.A twostage Patankar procedure for each Runge-Kutta step is designed to eliminate the first-order truncation terms,accomplish the prior third order of accuracy and maximize the Courant number which the total variational diminishing property requires.With the same approach as the second-order schemes,the third-order ones are applied to Euler equations with chemical reactive source terms.Numerical studies including both 1D and 2D ordinary and partial differential equations are conducted to affirm both the prior order of accuracy and the positivity-preserving property for the density and pressure.展开更多
We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH nume...We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.展开更多
文摘ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lewy (CFL) coefficient. Toro and Titarev employed CCFL=0.95for their experiments. Nonetheless, we noted that the experiments conducted in this study with CCFL=0.95produced solutions exhibiting spurious oscillations, particularly in the high-order ADER-WAF schemes. The homogeneous one-dimensional (1D) non-linear Shallow Water Equations (SWEs) are the subject of these experiments, specifically the solution of the Riemann Problem (RP) associated with the SWEs. The investigation was conducted on four test problems to evaluate the ADER-WAF schemes of second, third, fourth, and fifth order of accuracy. Each test problem constitutes a RP characterized by different wave patterns in its solution. This research has two primary objectives. We begin by illustrating the procedure for implementing the ADER-WAF schemes for the SWEs, providing the required relations. Afterward, following comprehensive testing, we present the range for the CFL coefficient for each test that yields solutions with diminished or eliminated spurious oscillations.
基金Science and Technology Research Project of Guang-dong Meteorological Bureau(GRMC2022M21)Guangdong Basic and Applied Basic Research Foundation(2023A1515012240)Research Project of Guangzhou Meteor-ological Bureau(M202218)。
文摘Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.
文摘International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper integrates the existing research of international carbon tax scholars to the classification and comparative analysis of international carbon tax schemes.Using a literature review approach,this dissertation mainly applies the method of qualitative analysis to explain and compare the contents of four international carbon tax options.Through the analysis and evaluation of individual countries’carbon tax practice,the two-country model is verified.Through the method of comparative analysis,the schemes are evaluated from four dimensions and an assessment is made.The difference of carbon tax among countries makes the internal policies of countries adjust accordingly with the changes of international environment,which promotes the gradual convergence of carbon tax schemes.The results intend to provide reference to further study the issue on international carbon tax.
基金supported by the National Natural Science Foundation of China(Grant No.42305169)the Basic Research Fund of CAMS(Grant No.2023Y001)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab)。
文摘Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.
基金supported by Grant PID2020-117211GB-I00funded by MCIN/AEI/10.13039/501100011033+4 种基金by Grant CIAICO/2021/227funded by the Generalitat Valencianasupported by the Ministerio de Ciencia e Innovacion of Spain(Grant Ref.PID2021-125709OB-C21)funded by MCIN/AEI/10.13039/501100011033/FEDER,UEby the Generalitat Valenciana(CIAICO/2021/224).
文摘Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.
基金Research was supported in part by the ONR Grant N00014-2112773.
文摘Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.
文摘Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
文摘In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.
基金Initiative 2018–2027 attributed to DICAM of the University of Trento(grant L.232/2016)the PRIN 2022 project High-order structure-preserving semi-implicit schemes for hyperbolic equations and by the European Union-Next GenerationEU(PNRR,Spoke 7 CN HPC).
文摘This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.
基金The project supported by the National Natural Science Foundation of China (19582007) Partly by State Key Laboratory of Scientific/Engineering Computing
文摘By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)
文摘A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.
基金supported by the NSFC grant 11801143J.Lu’s research is partially supported by the NSFC grant 11901213+3 种基金the National Key Research and Development Program of China grant 2021YFA1002900supported by the NSFC grant 11801140,12171177the Young Elite Scientists Sponsorship Program by Henan Association for Science and Technology of China grant 2022HYTP0009the Program for Young Key Teacher of Henan Province of China grant 2021GGJS067.
文摘This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.
文摘In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the main contributor to the stability of the slope.Then,two widening schemes are proposed,which are the steep slope with strong support and the gentle slope with general support schemes.The static/slope module of MIDAS GTS finite element analysis software and the strength reduction method were used to compare the two schemes.The results show that the steep slope with a strong support scheme has obvious advantages in land requisition,environmental protection,and safety and is more suitable for reconstructing and expanding the highway slope.
基金Supported by National Key R&D Program of China (Grant No.2023YFB3407103)National Natural Science Foundation of China (Grant Nos.52175242,52175027)Young Elite Scientists Sponsorship Program by CAST (Grant No.2022QNRC001)。
文摘Mesh reflector antennas are widely used in space tasks owing to their light weight,high surface accuracy,and large folding ratio.They are stowed during launch and then fully deployed in orbit to form a mesh reflector that transmits signals.Smooth deployment is essential for duty services;therefore,accurate and efficient dynamic modeling and analysis of the deployment process are essential.One major challenge is depicting time-varying resistance of the cable network and capturing the cable-truss coupling behavior during the deployment process.This paper proposes a general dynamic analysis methodology for cable-truss coupling.Considering the topological diversity and geometric nonlinearity,the cable network's equilibrium equation is derived,and an explicit expression of the time-varying tension of the boundary cables,which provides the main resistance in truss deployment,is obtained.The deployment dynamic model is established,which considers the coupling effect between the soft cables and deployable truss.The effects of the antenna's driving modes and parameters on the dynamic deployment performance were investigated.A scaled prototype was manufactured,and the deployment experiment was conducted to verify the accuracy of the proposed modeling method.The proposed methodology is suitable for general cable antennas with arbitrary topologies and parameters,providing theoretical guidance for the dynamic performance evaluation of antenna driving schemes.
基金supported by the Simons Foundation:Collaboration Grantssupported by the AFOSR grant FA9550-18-1-0383.
文摘In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.
基金supported by NSFC(No.41174118)one of the major state S&T special projects(No.2008ZX05020-004)+1 种基金a Postdoctoral Fellowship of China(No.2013M530106)China Scholarship Council(No.2010644006)
文摘In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.
基金Supported by the National Natural Defense Basic Scientific Research Program of China(A262006-1288)the Key Disciplines Program of Shanghai Municipal Commission of Education(J50501)~~
文摘Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.
文摘The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step size is chosen based on the size of the background cells.In May and Berger(J Sci Comput 71:919–943,2017),the mixed explicit-implicit approach in general and MUSCL-Trap(monotonic upwind scheme for conservation laws and trapezoidal scheme)in particular have been introduced to solve this problem by using implicit time stepping on the cut cells.Theoretical and numerical results have indicated that this might lead to a loss in accuracy when switching between the explicit and implicit time stepping.In this contribution,we examine this in more detail and will prove in one dimension that the specific combination MUSCL-Trap of an explicit second-order and an implicit second-order scheme results in a fully second-order mixed scheme.As this result is unlikely to hold in two dimensions,we also introduce two new versions of mixed explicit-implicit schemes based on exchanging the explicit scheme.We present numerical tests in two dimensions where we compare the new versions with the original MUSCL-Trap scheme.
基金This work was supported by the National Natural Science Foundation of China(No.12102211)the Science and Technology Innovation 2025 Major Project of Ningbo,China(No.2022Z213).
文摘In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,the mass conservation,mole balance and energy conservation are kept simultaneously while the positivity for the density and pressure is preserved unconditionally even with stiff reaction networks.It is proved that the first-order truncation terms for the Patankar coefficients must be zero to achieve a prior third order of accuracy for most cases.A twostage Patankar procedure for each Runge-Kutta step is designed to eliminate the first-order truncation terms,accomplish the prior third order of accuracy and maximize the Courant number which the total variational diminishing property requires.With the same approach as the second-order schemes,the third-order ones are applied to Euler equations with chemical reactive source terms.Numerical studies including both 1D and 2D ordinary and partial differential equations are conducted to affirm both the prior order of accuracy and the positivity-preserving property for the density and pressure.
基金The work of B.S.Wang and W.S.Don was partially supported by the Ocean University of China through grant 201712011The work of A.Kurganov was supported in part by NSFC grants 11771201 and 1201101343by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.
