Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these met...Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.展开更多
Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a...Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.展开更多
A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an o...A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.展开更多
This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative...This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.展开更多
Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to ...Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.展开更多
The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on several examples.
In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obt...In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.展开更多
The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in...The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in the expression,which approximates the term with spatial derivatives.The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter.For the proper choice of the parameter,these functions are minimized.The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term.The cases of schemes from first to fourth approximation orders are considered.The optimal values of the parameter are obtained.Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions.Also,schemes are used in the FD-based lattice Boltzmann method(LBM)for modeling of the compressible gas flow.The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.展开更多
3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic m...3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.展开更多
The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order sy...The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.展开更多
An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D tra...An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.展开更多
An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete fo...An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.展开更多
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
In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interfac...In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interface capturing(THINC)technique.We employ boundary variation diminishing(BVD)reconstruction to enhance the scheme’s effectiveness in handling shocks.First,we prove that wavelet collocation upwind schemes based on interpolating wavelets can be reformulated into a conservative form within the framework of wavelet theory,forming the foundation of the proposed scheme.The new fourthorder accurate scheme possesses significantly better spectral resolution than the fifth-and even seventh-order WENO-Z(weighted essentially non-oscillatory)schemes over the entire wave-number range.Moreover,the inherent low-pass filtering property of the wavelet bases allows them to filter high-frequency numerical oscillations,endowing the wavelet upwind scheme with robustness and accuracy in solving problems under extreme conditions.Notably,due to the wavelet multiresolution approximation,the proposed scheme possesses a distinctive shape-preserving property absent in the WENO-Z schemes and the fifth-order schemes with BVD reconstruction based on polynomials.Furthermore,compared to the fifth-order scheme with BVD reconstruction based on polynomials—which is significantly superior to the WENO schemes—the proposed scheme further enhances the ability to capture discontinuities.展开更多
Numerical models play an important role in convective-scale forecasting,and dual-polarization radar observations can provide detailed microphysical data.In this study,we implement a direct assimilation operator for du...Numerical models play an important role in convective-scale forecasting,and dual-polarization radar observations can provide detailed microphysical data.In this study,we implement a direct assimilation operator for dual-polarization radar data using the hydrometeor background error covariance(HBEC)in the China Meteorological Administration MESO-scale weather forecasting system(CMA-MESO,formerly GRAPES-MESO)and conducted assimilation and forecasting experiments with X-band and S-band dual-polarization radar data on two cases.The results indicate that the direct assimilation of dual-polarization radar data enhanced the microphysical fields and the thermodynamic structure of convective systems to some extent based on the HBEC,thereby improving precipitation forecasts.Among the sensitivity tests of microphysical parameterization schemes,including the LIUMA scheme,the THOMPSON scheme,and the WSM6scheme(WRF Single-Moment 6-class),we find that the greatest improvement in the equivalent potential temperature,relative humidity,wind,and accumulated precipitation forecasts occurred in the experiment using the WSM6 scheme,as the distribution of solid precipitation particles was closer to the hydrometeor classification algorithm from the dualpolarization radar observations in our cases.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
In this study,the Betts-Miller-Janjic(BMJ)convective adjustment scheme in the Weather Research and Forecasting(WRF)model version 4.0 was used to investigate the effect of itsα-parameter,which influences the first-gue...In this study,the Betts-Miller-Janjic(BMJ)convective adjustment scheme in the Weather Research and Forecasting(WRF)model version 4.0 was used to investigate the effect of itsα-parameter,which influences the first-guess potential temperature reference profile on the Madden-Julian oscillation(MJO)propagation and structure.This study diagnosed the MJO active phase composites of the MJO-filtered outgoing longwave radiation(OLR)during the December-to-February(DJF)period of 2006-2016 over the Indian Ocean(IO),Maritime Continent(MC),and western Pacific(WP).The results show that the MJO-filtered OLR intensity,propagation pattern,and MJO classification(standing,jumping,and propagating clusters)are sensitive to theα-value,but the phase speeds of propagating MJOs are not.Overall,with an increasingα-value,the simulated MJO-filtered OLR intensity increases,and the simulated propagation pattern is improved.Results also show that the intensity and propagation pattern of an eastward-propagating MJO are associated with MJO circulation structures and thermodynamic structures.Asαincreases,the front Walker cell and the low-level easterly anomaly are enhanced,which premoistens the lower troposphere and triggers more active shallow and congestus clouds.The enhanced shallow and congestus convection preconditions the lower to middle troposphere,accelerating the transition from congestus to deep convection,thereby facilitating eastward propagation of the MJO.Therefore,the simulated MJO tends to transfer from standing to eastward propagating asαincreases.In summary,increasing theα-value is a possible way to improve the simulation of the structure and propagation of the MJO.展开更多
The implementation of core competencies clarifies social talent needs and guides math classroom evaluation.Lower-grade primary students,highly malleable,need targeted teacher guidance.Teaching evaluation should meet t...The implementation of core competencies clarifies social talent needs and guides math classroom evaluation.Lower-grade primary students,highly malleable,need targeted teacher guidance.Teaching evaluation should meet the talent demands of the times,focusing on core literacy and essential character development.From this perspective,primary math teachers should optimize evaluation,build a diversified system,help students grow in math,find their learning position,and advance confidently.展开更多
Mesh reflector antennas are the mainstream of large space-borne antennas,and the stretching of the truss achieves their deployment.Currently,the truss is commonly designed to be a single degree of freedom(DOF)deployab...Mesh reflector antennas are the mainstream of large space-borne antennas,and the stretching of the truss achieves their deployment.Currently,the truss is commonly designed to be a single degree of freedom(DOF)deployable mechanism with synchronization constraints.However,each deployable unit’s drive distribution and resistance load are uneven,and the forced synchronization constraints lead to the flexible deformation of rods and difficulties in the deployment scheme design.This paper introduces an asynchronous deployment scheme with a multi-DOF closed-chain deployable truss.The DOF of the truss is calculated,and the kinematic and dynamic models are established,considering the truss’s and cable net’s real-time coupling.An integrated solving algorithm for implicit differential-algebraic equations is proposed to solve the dynamic models.A prototype of a six-unit antenna was fabricated,and the experiment was carried out.The dynamic performances in synchronous and asynchronous deployment schemes are analyzed,and the results show that the cable resistance and truss kinetic energy impact under the asynchronous deployment scheme are minor,and the antenna is more straightforward to deploy.The work provides a new asynchronous deployment scheme and a universal antenna modeling method for dynamic design and performance improvement.展开更多
Shale oil reservoir is generally characterized by well-developed bedding planes,and multi-cluster fracturing is the most effective technique to achieve stable shale oil production.In this paper,a multi-cluster fractur...Shale oil reservoir is generally characterized by well-developed bedding planes,and multi-cluster fracturing is the most effective technique to achieve stable shale oil production.In this paper,a multi-cluster fracturing model for a horizontal well in shale with high-density bedding planes is established.The fracture morphology,fracture geometry,fracturing area and multiple fracture propagation mechanism are analyzed under simultaneous fracturing,sequential fracturing,and alternative fracturing.Results show that in the case of small cluster spacing and three clusters,the growth of the middle fracture is inhibited and develops along the bedding planes under both simultaneous fracturing and alternative fracturing.For sequential fracturing,the increase in the interval time between each fracturing advances the post fracturing fracture deflecting to the pre-existing fractures through the bedding planes.The reactivation of the bedding planes can promote the extension of the fracturing area.Increasing the injection rate and the number of clusters promotes the activation of bedding planes.However,it is preferable to reduce the number of clusters to obtain more main fractures.Compared with modified alternating fracturing and cyclic alternating fracturing,alternating shut-in fracturing creates more main fractures towards the direction of the maximum in-situ stress.The fracturing efficiency for high-density layered shale is ranked as simultaneous fracturing>alternative fracturing>sequential fracturing.展开更多
基金This research is supported by the National Natural Science Foundation of China(NSFC)under contract no.42274147.
文摘Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.
基金supported by the National Natural Science Foundation of China(No.41474110)Shell Ph.D. Scholarship to support excellence in geophysical research
文摘Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.
基金Project supported by the National Natural Science Foundation of China(Nos.11601517,11502296,61772542,and 61561146395)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.
文摘This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.
文摘Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.
文摘The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on several examples.
文摘In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.
文摘The approach to optimization of finite-difference(FD)schemes for the linear advection equation(LAE)is proposed.The FD schemes dependent on the scalar dimensionless parameter are considered.The parameter is included in the expression,which approximates the term with spatial derivatives.The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter.For the proper choice of the parameter,these functions are minimized.The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term.The cases of schemes from first to fourth approximation orders are considered.The optimal values of the parameter are obtained.Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions.Also,schemes are used in the FD-based lattice Boltzmann method(LBM)for modeling of the compressible gas flow.The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.
基金The authors thank the funds supported by the China National Nuclear Corporation under Grants Nos.WUQNYC2101 and WUHTLM2101-04National Natural Science Foundation of China(42074132,42274154).
文摘3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.
基金supported by the National Natural Science Foundation of China(Grant Nos.60931002 and 61101064)the Universities Natural Science Foundation of Anhui Province,China(Grant Nos.KJ2011A002 and 1108085J01)
文摘The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.
基金supported by the National Natural Science Foundation of China(Grant Nos.61331007 and 61471105)
文摘An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.
基金the National Key Development and Planning Project for the Basic Research (973) (Grant No.2005CB321703)the Science Funds for Creative Research Groups (Grant No.40221503)
文摘An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.
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supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interface capturing(THINC)technique.We employ boundary variation diminishing(BVD)reconstruction to enhance the scheme’s effectiveness in handling shocks.First,we prove that wavelet collocation upwind schemes based on interpolating wavelets can be reformulated into a conservative form within the framework of wavelet theory,forming the foundation of the proposed scheme.The new fourthorder accurate scheme possesses significantly better spectral resolution than the fifth-and even seventh-order WENO-Z(weighted essentially non-oscillatory)schemes over the entire wave-number range.Moreover,the inherent low-pass filtering property of the wavelet bases allows them to filter high-frequency numerical oscillations,endowing the wavelet upwind scheme with robustness and accuracy in solving problems under extreme conditions.Notably,due to the wavelet multiresolution approximation,the proposed scheme possesses a distinctive shape-preserving property absent in the WENO-Z schemes and the fifth-order schemes with BVD reconstruction based on polynomials.Furthermore,compared to the fifth-order scheme with BVD reconstruction based on polynomials—which is significantly superior to the WENO schemes—the proposed scheme further enhances the ability to capture discontinuities.
基金sponsored by the National Natural Science Foundation of China(U2442601 and U2442218)the High Performance Computing Platform of Nanjing University of Information Science&Technology(NUIST)for their support of this work。
文摘Numerical models play an important role in convective-scale forecasting,and dual-polarization radar observations can provide detailed microphysical data.In this study,we implement a direct assimilation operator for dual-polarization radar data using the hydrometeor background error covariance(HBEC)in the China Meteorological Administration MESO-scale weather forecasting system(CMA-MESO,formerly GRAPES-MESO)and conducted assimilation and forecasting experiments with X-band and S-band dual-polarization radar data on two cases.The results indicate that the direct assimilation of dual-polarization radar data enhanced the microphysical fields and the thermodynamic structure of convective systems to some extent based on the HBEC,thereby improving precipitation forecasts.Among the sensitivity tests of microphysical parameterization schemes,including the LIUMA scheme,the THOMPSON scheme,and the WSM6scheme(WRF Single-Moment 6-class),we find that the greatest improvement in the equivalent potential temperature,relative humidity,wind,and accumulated precipitation forecasts occurred in the experiment using the WSM6 scheme,as the distribution of solid precipitation particles was closer to the hydrometeor classification algorithm from the dualpolarization radar observations in our cases.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.41975090,U2242201,42075077)the Natural Science Foundation of Hunan Province,China(2022JJ20043)the Science and Technology Innovation Program of Hunan Province,China(2022RC1239)。
文摘In this study,the Betts-Miller-Janjic(BMJ)convective adjustment scheme in the Weather Research and Forecasting(WRF)model version 4.0 was used to investigate the effect of itsα-parameter,which influences the first-guess potential temperature reference profile on the Madden-Julian oscillation(MJO)propagation and structure.This study diagnosed the MJO active phase composites of the MJO-filtered outgoing longwave radiation(OLR)during the December-to-February(DJF)period of 2006-2016 over the Indian Ocean(IO),Maritime Continent(MC),and western Pacific(WP).The results show that the MJO-filtered OLR intensity,propagation pattern,and MJO classification(standing,jumping,and propagating clusters)are sensitive to theα-value,but the phase speeds of propagating MJOs are not.Overall,with an increasingα-value,the simulated MJO-filtered OLR intensity increases,and the simulated propagation pattern is improved.Results also show that the intensity and propagation pattern of an eastward-propagating MJO are associated with MJO circulation structures and thermodynamic structures.Asαincreases,the front Walker cell and the low-level easterly anomaly are enhanced,which premoistens the lower troposphere and triggers more active shallow and congestus clouds.The enhanced shallow and congestus convection preconditions the lower to middle troposphere,accelerating the transition from congestus to deep convection,thereby facilitating eastward propagation of the MJO.Therefore,the simulated MJO tends to transfer from standing to eastward propagating asαincreases.In summary,increasing theα-value is a possible way to improve the simulation of the structure and propagation of the MJO.
文摘The implementation of core competencies clarifies social talent needs and guides math classroom evaluation.Lower-grade primary students,highly malleable,need targeted teacher guidance.Teaching evaluation should meet the talent demands of the times,focusing on core literacy and essential character development.From this perspective,primary math teachers should optimize evaluation,build a diversified system,help students grow in math,find their learning position,and advance confidently.
基金supported by the National Key R&D Program of China(Grant No.2023YFB3407103)the National Natural Science Foundation of China(Grant Nos.52175242 and 52175027)Young Elite Scientists Sponsorship Program by China Association for Science and Technology(Grant No.2022QNRC001).
文摘Mesh reflector antennas are the mainstream of large space-borne antennas,and the stretching of the truss achieves their deployment.Currently,the truss is commonly designed to be a single degree of freedom(DOF)deployable mechanism with synchronization constraints.However,each deployable unit’s drive distribution and resistance load are uneven,and the forced synchronization constraints lead to the flexible deformation of rods and difficulties in the deployment scheme design.This paper introduces an asynchronous deployment scheme with a multi-DOF closed-chain deployable truss.The DOF of the truss is calculated,and the kinematic and dynamic models are established,considering the truss’s and cable net’s real-time coupling.An integrated solving algorithm for implicit differential-algebraic equations is proposed to solve the dynamic models.A prototype of a six-unit antenna was fabricated,and the experiment was carried out.The dynamic performances in synchronous and asynchronous deployment schemes are analyzed,and the results show that the cable resistance and truss kinetic energy impact under the asynchronous deployment scheme are minor,and the antenna is more straightforward to deploy.The work provides a new asynchronous deployment scheme and a universal antenna modeling method for dynamic design and performance improvement.
基金the financial support from Intergovernmental International Science and Technology Innovation Cooperation Key Project(2022YFE0128400)National Natural Science Foundation of China(42307209)+2 种基金Shanghai Pujiang Program(2022PJD076)State Energy Center for Shale Oil Research and Development(33550000-22-ZC0613-0365)Natural Science Foundation of Qinghai Province(No.2024-ZJ-717).
文摘Shale oil reservoir is generally characterized by well-developed bedding planes,and multi-cluster fracturing is the most effective technique to achieve stable shale oil production.In this paper,a multi-cluster fracturing model for a horizontal well in shale with high-density bedding planes is established.The fracture morphology,fracture geometry,fracturing area and multiple fracture propagation mechanism are analyzed under simultaneous fracturing,sequential fracturing,and alternative fracturing.Results show that in the case of small cluster spacing and three clusters,the growth of the middle fracture is inhibited and develops along the bedding planes under both simultaneous fracturing and alternative fracturing.For sequential fracturing,the increase in the interval time between each fracturing advances the post fracturing fracture deflecting to the pre-existing fractures through the bedding planes.The reactivation of the bedding planes can promote the extension of the fracturing area.Increasing the injection rate and the number of clusters promotes the activation of bedding planes.However,it is preferable to reduce the number of clusters to obtain more main fractures.Compared with modified alternating fracturing and cyclic alternating fracturing,alternating shut-in fracturing creates more main fractures towards the direction of the maximum in-situ stress.The fracturing efficiency for high-density layered shale is ranked as simultaneous fracturing>alternative fracturing>sequential fracturing.
