The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω i...The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω is a bounded open set in Rn with smoothbonndary and the nonlinearity bu+ crosses eigenvalues of △2 ＋c△. They investigate therelatiolls when the source term is constant and when it is generated by two eigenfuntions.展开更多
Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption...The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.展开更多
Nowadays, chemical safety has attracted considerable attention, and chemical gas leakage monitoring and source term estimation(STE) have become hot spots. However, few studies have focused on sensor layouts in scenari...Nowadays, chemical safety has attracted considerable attention, and chemical gas leakage monitoring and source term estimation(STE) have become hot spots. However, few studies have focused on sensor layouts in scenarios with multiple potential leakage sources and wind conditions, and studies on the risk information(RI) detection and prioritization order of sensors have not been performed. In this work, the monitoring area of a chemical factory is divided into multiple rectangles with a uniform mesh. The RI value of each grid node is calculated on the basis of the occurrence probability and normalized concentrations of each leakage scenario. A high RI value indicates that a sensor at a grid node has a high chance of detecting gas concentrations in different leakage scenarios. This situation is beneficial for leakage monitoring and STE. The methods of similarity redundancy detection and the maximization of sensor RI detection are applied to determine the sequence of sensor locations. This study reveals that the RI detection of the optimal sensor layout with eight sensors exceeds that of the typical layout with 12 sensors. In addition, STE with the optimized placement sequence of the sensor layout is numerically simulated. The statistical results of each scenario with various numbers of sensors reveal that STE is affected by sensor number and scenarios(leakage locations and winds). In most scenarios, appropriate STE results can be retained under the optimal sensor layout even with four sensors. Eight or more sensors are advised to improve the performance of STE in all scenarios. Moreover, the reliability of the STE results in each scenario can be known in advance with a specific number of sensors. Such information thus provides a reference for emergency rescue.展开更多
Considering the growing global demand for energy and the need for countries to achieve climate goals,there is an increasing global interest in small modular reactors(SMRs)and their applications.Accident source term an...Considering the growing global demand for energy and the need for countries to achieve climate goals,there is an increasing global interest in small modular reactors(SMRs)and their applications.Accident source term and radiological consequence evaluations of SMRs are key components of nuclear and radiation safety reviews,which affect the site,exclusion area(EAB),and low population zone outer boundaries.Based on the design characteristics of the SMR and accident analysis results,a theoretical model of a whole-core fuel cladding damage accident was constructed to study the radioactivity released into the environment and its consequences.The accident source term and radiation dose calculation models were established to analyze the released amounts of radionuclides and the total effective dose affecting individuals at the site boundary.The results showed that the amount of radionuclides released into the environment after a whole-core fuel cladding damage accident reached 10^(14) Bq,among which the release amount of ^(133)Xe was the largest.The total effective dose at the site boundary 30 days after the accident was 8.65 mSv.The highest total effective dose affecting individuals occurred to the east-north-east.The results of the accident source term and radiological consequence provide technical support for site boundary dose assessments and reviews of SMRs.展开更多
This study proposes a source distribution inversion convolutional neural network (SDICNN), which is deep neural network model for the inversion of complex source distributions, to solve inversion problems involving fi...This study proposes a source distribution inversion convolutional neural network (SDICNN), which is deep neural network model for the inversion of complex source distributions, to solve inversion problems involving fixed-source distributions. A function is developed to obtain the distribution information of complex source terms from radiation parameters at individual sampling points in space. The SDICNN comprises two components:a fully connected network and a convolutional neural network. The fully connected network mainly extracts the parameter measurement information from the sampling points,whereas the convolutional neural network mainly completes the fine inversion of the source-term distribution. Finally, the SDICNN obtains a high-resolution source-term distribution image. In this study, the proposed source-term inversion method is evaluated based on typical geometric scenarios. The results show that, unlike the conventional fully connected neural network, the SDICNN model can extract the two-dimensional distribution features of the source terms, and its inversion results are better. In addition, the effects of the shielding mechanism and number of sampling points on the inversion process are examined. In summary, the result of this study can facilitate the accurate assessment of dose distributions in nuclear facilities.展开更多
In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional...In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.展开更多
Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an impr...Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.展开更多
In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving...In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.展开更多
In this paper,we investigate the initial boundary value problem for a plate equation with nonlocal source term.The local,global existence and exponential decay result are established under certain conditions.Moreover,...In this paper,we investigate the initial boundary value problem for a plate equation with nonlocal source term.The local,global existence and exponential decay result are established under certain conditions.Moreover,we also prove the blow-up in finite time and the lifespan of solution under certain conditions.展开更多
A computational fluid dynamics( CFD) model was presented to simulate wind flow over a forest canopy for analyzing the wind flow within and above forest canopies. Unlike previous studies on the canopy flow,the effect o...A computational fluid dynamics( CFD) model was presented to simulate wind flow over a forest canopy for analyzing the wind flow within and above forest canopies. Unlike previous studies on the canopy flow,the effect of canopy contour on the canopy was considered to develop the simulation method into a more general but complex case of wind flow over a forest canopy,using cedrus deodara and cinnamomum camphora. The desire of this work is mainly motivated to provide a rational way for predicting the wind flow within and above vegetation canopies. The model of canopy is not incorporated in the geometrical model,and it uses a porous domain combined with k-ε two-equation turbulence model with source / sink terms. The objectives of this paper are to analyze the contour of pressure and velocity and compare the simulation results with other works and field measurements. Results are encouraging,as the model profiles of mean velocity( u) qualitatively agree well with other works compared with and quantitatively have similar explanations as several authors. In conclusion, it is demonstrated that the adoption turbulence model with source / sink terms for forest canopies is proved to be a physically accurate and numerically robust method. The model and method are recommended for future use in simulating turbulent flows in forest canopies.展开更多
In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to so...In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.展开更多
Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of ...Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.展开更多
In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosi...In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.展开更多
Wave climate analysis and other applications for the Pacific Ocean require a reliable wave hindcast. Five source and sink term packages in the Wavewatch III model （v3.14 and v4.18） are compared and assessed in this ...Wave climate analysis and other applications for the Pacific Ocean require a reliable wave hindcast. Five source and sink term packages in the Wavewatch III model （v3.14 and v4.18） are compared and assessed in this study through comprehensive observations, including altimeter significant wave height, advanced synthetic aperture radar swell, and buoy wave parameters and spectrum. In addition to the evaluation of typically used integral parameters, the spectra partitioning method contributes to the detailed wave system and wave maturity validation. The modified performance evaluation method （PS） effectively reduces attribute numbers and facilitates the overall assessment. To avoid possible misleading results in the root mean square error-based validations, another indicator called HH （indicating the two authors） is also calculated to guarantee the consistency of the results. The widely used Tolman and Chalikov （TC） package is still generally efficient in determining the integral properties of wave spectra but is physically deficient in explaining the dissipation processes. The ST4 package performs well in overall wave parameters and significantly improves the accuracy of wave systems in the open ocean. Meanwhile, the newly published ST6 package is slightly better in determining swell energy variations. The two packages （ACC350 and BIA） obtained from Wavewatch III v3.14 exhibit large scatters at different sea states. The three most ideal packages are further examined in terms of reproducing wave- induced momentum flux from the perspective of transport. Stokes transport analysis indicates that ST4 is the closest to the NDBC-buoy-spectrum-based transport values, and TC and ST6 tend to overestimate and underestimate the transport magnitude, respectively, in swell mixed areas. This difference must be considered, particularly in air-wave-current coupling research and upper ocean analysis. The assessment results provide guidance for the selection of ST4 for use in a background Pacific Ocean hindcast for high wave climate research and China Sea swell type analysis.展开更多
In this study,a numerical flow model of the fission products(FPs)in the primary loop system of a molten salt reactor(MSR)was established and solved using Mathematica 7.0.The simulation results were compared with those...In this study,a numerical flow model of the fission products(FPs)in the primary loop system of a molten salt reactor(MSR)was established and solved using Mathematica 7.0.The simulation results were compared with those of the ORIGEN-S program in the static burnup mode,and the deviation was found to be less than 10%,which indicates that the results are in good agreement.Furthermore,the FPs distribution in the primary loop system under normal operating conditions of the 2 MW MSR was quantitatively analyzed.In addition,the distribution phenomenon of the FPs under different flow rate conditions was studied.At the end of life,the FPs activity in the core region(including active region,and upper and lower plenum regions)accounted for 77.3%,and that in the hot leg #1,main pump,hot leg #2,heat exchanger,and cold leg region accounted for 1.2%,16.15%,0.99%,2.5%,and 1.9%,respectively,of the total FPs in the primary loop under normal operating conditions.The proportion of FPs in the core decreased with the increase in flow rate in the range of 2.24-22,400 cm^3 s^-1.The established analytical method and conclusions of this study can provide an important basis for radiation safety design of the primary loop,radioactive source management design,thermal-hydraulic safety analysis,and radiochemical analysis of FPs of 2 MW MSRs.展开更多
In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential ine...In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential inequality techniques are used to obtain the lower bounds on the blow up time of the equation set under two different boundary conditions.展开更多
Extensive studies have been carried out on the behavior of core degradation and fission products of common pressurized water reactors(PWRs).However,few of them have investigated the relationship between thermal hydrau...Extensive studies have been carried out on the behavior of core degradation and fission products of common pressurized water reactors(PWRs).However,few of them have investigated the relationship between thermal hydraulic and fission product behavior in advanced passive PWRs.Due to the impact of thermal hydraulic be-haviors in different accident sequences on the release and transportation of fission products,an integrated severe accident analysis(ISAA)code with highly coupled thermal hydraulic and source term calculations is required to simultaneously analyze thermal hydraulic and source term behavior.For advanced passive PWRs,important safety systems that may affect the behavior of the core and fission products should be considered.It is therefore necessary to simulate the thermal hydraulic and fission product behavior of advanced passive PWRs.In this study,the ISAA code is adopted to simulate the occurrence of a hypothetical double ended cold leg LBLOCA of HPR1000 in three scenarios of equipment failure.The results show that the high-temperature fuel rods and cladding ma-terials exhibit delayed failure at the lower position of the active core,whereas earlier failure at higher position during the reflooding.Active and passive equipment affects fuel temperature,the oxidation conditions of the fuel,the interaction of fission products and structural materials,and the state of the fuel,thereby affecting the release of fission products in the fuel.HPR1000 only relies on passive equipment to relieve the core degradation in severe accidents,realize the in-vessel retention of melt,and eliminate the ex-vessel release possibility of fission product.It is hoped that the results can provide references for HPR1000 to formulate the severe accident management guidelines(SAMG).展开更多
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a cl...Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms.In this paper,we present a different approach to the same purpose:designing high order well-balanced finite volume weighted essentially non-oscillatory(WENO)schemes and RungeKutta discontinuous Galerkin(RKDG)finite element methods.We make the observation that the traditional RKDG methods are capable of maintaining certain steady states exactly,if a small modification on either the initial condition or the flux is provided.The computational cost to obtain such a well balanced RKDG method is basically the same as the traditional RKDG method.The same idea can be applied to the finite volume WENO schemes.We will first describe the algorithms and prove the well balanced property for the shallow water equations,and then show that the result can be generalized to a class of other balance laws.We perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions,the non-oscillatory property for general solutions with discontinuities,and the genuine high order accuracy in smooth regions.展开更多
文摘The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω is a bounded open set in Rn with smoothbonndary and the nonlinearity bu+ crosses eigenvalues of △2 ＋c△. They investigate therelatiolls when the source term is constant and when it is generated by two eigenfuntions.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
基金Supported by the National S&T Major Project under Grant No.ZX06901
文摘The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.
基金supported by National Natural Science Foundation of China (61988101)National Natural Science Fund for Distinguished Young Scholars (61725301)Fundamental Research Funds for the Central Universities。
文摘Nowadays, chemical safety has attracted considerable attention, and chemical gas leakage monitoring and source term estimation(STE) have become hot spots. However, few studies have focused on sensor layouts in scenarios with multiple potential leakage sources and wind conditions, and studies on the risk information(RI) detection and prioritization order of sensors have not been performed. In this work, the monitoring area of a chemical factory is divided into multiple rectangles with a uniform mesh. The RI value of each grid node is calculated on the basis of the occurrence probability and normalized concentrations of each leakage scenario. A high RI value indicates that a sensor at a grid node has a high chance of detecting gas concentrations in different leakage scenarios. This situation is beneficial for leakage monitoring and STE. The methods of similarity redundancy detection and the maximization of sensor RI detection are applied to determine the sequence of sensor locations. This study reveals that the RI detection of the optimal sensor layout with eight sensors exceeds that of the typical layout with 12 sensors. In addition, STE with the optimized placement sequence of the sensor layout is numerically simulated. The statistical results of each scenario with various numbers of sensors reveal that STE is affected by sensor number and scenarios(leakage locations and winds). In most scenarios, appropriate STE results can be retained under the optimal sensor layout even with four sensors. Eight or more sensors are advised to improve the performance of STE in all scenarios. Moreover, the reliability of the STE results in each scenario can be known in advance with a specific number of sensors. Such information thus provides a reference for emergency rescue.
文摘Considering the growing global demand for energy and the need for countries to achieve climate goals,there is an increasing global interest in small modular reactors(SMRs)and their applications.Accident source term and radiological consequence evaluations of SMRs are key components of nuclear and radiation safety reviews,which affect the site,exclusion area(EAB),and low population zone outer boundaries.Based on the design characteristics of the SMR and accident analysis results,a theoretical model of a whole-core fuel cladding damage accident was constructed to study the radioactivity released into the environment and its consequences.The accident source term and radiation dose calculation models were established to analyze the released amounts of radionuclides and the total effective dose affecting individuals at the site boundary.The results showed that the amount of radionuclides released into the environment after a whole-core fuel cladding damage accident reached 10^(14) Bq,among which the release amount of ^(133)Xe was the largest.The total effective dose at the site boundary 30 days after the accident was 8.65 mSv.The highest total effective dose affecting individuals occurred to the east-north-east.The results of the accident source term and radiological consequence provide technical support for site boundary dose assessments and reviews of SMRs.
基金supported by the Platform Development Foundation of the China Institute for Radiation Protection (No. YP21030101)the National Natural Science Foundation of China (General Program)(Nos. 12175114, U2167209)+1 种基金the National Key R&D Program of China (No. 2021YFF0603600)the Tsinghua University Initiative Scientific Research Program (No. 20211080081)。
文摘This study proposes a source distribution inversion convolutional neural network (SDICNN), which is deep neural network model for the inversion of complex source distributions, to solve inversion problems involving fixed-source distributions. A function is developed to obtain the distribution information of complex source terms from radiation parameters at individual sampling points in space. The SDICNN comprises two components:a fully connected network and a convolutional neural network. The fully connected network mainly extracts the parameter measurement information from the sampling points,whereas the convolutional neural network mainly completes the fine inversion of the source-term distribution. Finally, the SDICNN obtains a high-resolution source-term distribution image. In this study, the proposed source-term inversion method is evaluated based on typical geometric scenarios. The results show that, unlike the conventional fully connected neural network, the SDICNN model can extract the two-dimensional distribution features of the source terms, and its inversion results are better. In addition, the effects of the shielding mechanism and number of sampling points on the inversion process are examined. In summary, the result of this study can facilitate the accurate assessment of dose distributions in nuclear facilities.
基金supported by the National Natural Science Foundation of China(11961044)the Doctor Fund of Lan Zhou University of Technologythe Natural Science Foundation of Gansu Provice(21JR7RA214)。
文摘In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.
基金Ministry of Science and Technology of the People’s Republic of China for its support and guidance(Grant No.2018YFC0214100)。
文摘Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.
基金the Council of Scientific and Industrial Research,New Delhi,India for its financial support.
文摘In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.
基金Supported by National Natural Science Foundation of China(11801145)Key Scientific Research Foundation of the Higher Education Institutions of Henan Province,China(Grant No.19A110004)and(2018GGJS068)。
文摘In this paper,we investigate the initial boundary value problem for a plate equation with nonlocal source term.The local,global existence and exponential decay result are established under certain conditions.Moreover,we also prove the blow-up in finite time and the lifespan of solution under certain conditions.
基金National Natural Science Foundations of China(Nos.51178094,41371445)
文摘A computational fluid dynamics( CFD) model was presented to simulate wind flow over a forest canopy for analyzing the wind flow within and above forest canopies. Unlike previous studies on the canopy flow,the effect of canopy contour on the canopy was considered to develop the simulation method into a more general but complex case of wind flow over a forest canopy,using cedrus deodara and cinnamomum camphora. The desire of this work is mainly motivated to provide a rational way for predicting the wind flow within and above vegetation canopies. The model of canopy is not incorporated in the geometrical model,and it uses a porous domain combined with k-ε two-equation turbulence model with source / sink terms. The objectives of this paper are to analyze the contour of pressure and velocity and compare the simulation results with other works and field measurements. Results are encouraging,as the model profiles of mean velocity( u) qualitatively agree well with other works compared with and quantitatively have similar explanations as several authors. In conclusion, it is demonstrated that the adoption turbulence model with source / sink terms for forest canopies is proved to be a physically accurate and numerically robust method. The model and method are recommended for future use in simulating turbulent flows in forest canopies.
基金the European Union’s NextGenerationUE-Project:Centro Nazionale HPC,Big Data e Quantum Computing,“Spoke 1”(No.CUP E63C22001000006)E.Macca was partially supported by GNCS No.CUP E53C22001930001 Research Project“Metodi numericiper problemi differenziali multiscala:schemi di alto ordine,ottimizzazione,controllo”+1 种基金E.Macca and S.Boscarino would like to thank the Italian Ministry of Instruction,University and Research(MIUR)to supportthis research with funds coming from PRIN Project 2022(2022KA3JBA,entitled“Advanced numericalmethods for time dependent parametric partial differential equations and applications”)Sebastiano Boscarinohas been supported for this work from Italian Ministerial grant PRIN 2022 PNRR“FIN4GEO:forward andinverse numerical modeling of hydrothermalsystemsin volcanic regions with application to geothermal energyexploitation”(No.P2022BNB97).E.Macca and S.Boscarino are members of the INdAM Research groupGNCS.
文摘In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.
基金support via NSF grants NSF-19-04774,NSF-AST-2009776,NASA-2020-1241NASA grant 80NSSC22K0628.DSB+3 种基金HK acknowledge support from a Vajra award,VJR/2018/00129a travel grant from Notre Dame Internationalsupport via AFOSR grant FA9550-20-1-0055NSF grant DMS-2010107.
文摘Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.
基金supported by the National Natural Science Foundation of China (Grants No. 50909065 and 51109039)the National Basic Research Program of China (973 Program, Grant No. 2012CB417002)
文摘In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.
基金The National High Technology Research and Development Program(863 Program) of China under contract No.2013AA122803the Strategic Priority Research Program of the Chinese Academy of Sciences under contract No.XDA11010104
文摘Wave climate analysis and other applications for the Pacific Ocean require a reliable wave hindcast. Five source and sink term packages in the Wavewatch III model （v3.14 and v4.18） are compared and assessed in this study through comprehensive observations, including altimeter significant wave height, advanced synthetic aperture radar swell, and buoy wave parameters and spectrum. In addition to the evaluation of typically used integral parameters, the spectra partitioning method contributes to the detailed wave system and wave maturity validation. The modified performance evaluation method （PS） effectively reduces attribute numbers and facilitates the overall assessment. To avoid possible misleading results in the root mean square error-based validations, another indicator called HH （indicating the two authors） is also calculated to guarantee the consistency of the results. The widely used Tolman and Chalikov （TC） package is still generally efficient in determining the integral properties of wave spectra but is physically deficient in explaining the dissipation processes. The ST4 package performs well in overall wave parameters and significantly improves the accuracy of wave systems in the open ocean. Meanwhile, the newly published ST6 package is slightly better in determining swell energy variations. The two packages （ACC350 and BIA） obtained from Wavewatch III v3.14 exhibit large scatters at different sea states. The three most ideal packages are further examined in terms of reproducing wave- induced momentum flux from the perspective of transport. Stokes transport analysis indicates that ST4 is the closest to the NDBC-buoy-spectrum-based transport values, and TC and ST6 tend to overestimate and underestimate the transport magnitude, respectively, in swell mixed areas. This difference must be considered, particularly in air-wave-current coupling research and upper ocean analysis. The assessment results provide guidance for the selection of ST4 for use in a background Pacific Ocean hindcast for high wave climate research and China Sea swell type analysis.
基金supported by the Chinese Academy of Sciences TMSR Strategic Pioneer Science and Technology Project(No.XDA02010000)The Frontier Science Key Program of Chinese Academy of Sciences(No.QYZDY-SSW-JSC016)
文摘In this study,a numerical flow model of the fission products(FPs)in the primary loop system of a molten salt reactor(MSR)was established and solved using Mathematica 7.0.The simulation results were compared with those of the ORIGEN-S program in the static burnup mode,and the deviation was found to be less than 10%,which indicates that the results are in good agreement.Furthermore,the FPs distribution in the primary loop system under normal operating conditions of the 2 MW MSR was quantitatively analyzed.In addition,the distribution phenomenon of the FPs under different flow rate conditions was studied.At the end of life,the FPs activity in the core region(including active region,and upper and lower plenum regions)accounted for 77.3%,and that in the hot leg #1,main pump,hot leg #2,heat exchanger,and cold leg region accounted for 1.2%,16.15%,0.99%,2.5%,and 1.9%,respectively,of the total FPs in the primary loop under normal operating conditions.The proportion of FPs in the core decreased with the increase in flow rate in the range of 2.24-22,400 cm^3 s^-1.The established analytical method and conclusions of this study can provide an important basis for radiation safety design of the primary loop,radioactive source management design,thermal-hydraulic safety analysis,and radiochemical analysis of FPs of 2 MW MSRs.
基金Supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+3 种基金Project on Higher Education Teaching Reform of Xi’an International University(2019B36)Project of Qi Fang Education Research Institute of Xi’an International University(21mjy07)Special Project Support of the 14th Five Year Plan of the China Association of Higher Education(21DFD04)the Youth Innovation Team of Shaanxi Universities
文摘In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential inequality techniques are used to obtain the lower bounds on the blow up time of the equation set under two different boundary conditions.
基金the National Key Research and Development Program of China(Grant No.:2019YFE0191600).
文摘Extensive studies have been carried out on the behavior of core degradation and fission products of common pressurized water reactors(PWRs).However,few of them have investigated the relationship between thermal hydraulic and fission product behavior in advanced passive PWRs.Due to the impact of thermal hydraulic be-haviors in different accident sequences on the release and transportation of fission products,an integrated severe accident analysis(ISAA)code with highly coupled thermal hydraulic and source term calculations is required to simultaneously analyze thermal hydraulic and source term behavior.For advanced passive PWRs,important safety systems that may affect the behavior of the core and fission products should be considered.It is therefore necessary to simulate the thermal hydraulic and fission product behavior of advanced passive PWRs.In this study,the ISAA code is adopted to simulate the occurrence of a hypothetical double ended cold leg LBLOCA of HPR1000 in three scenarios of equipment failure.The results show that the high-temperature fuel rods and cladding ma-terials exhibit delayed failure at the lower position of the active core,whereas earlier failure at higher position during the reflooding.Active and passive equipment affects fuel temperature,the oxidation conditions of the fuel,the interaction of fission products and structural materials,and the state of the fuel,thereby affecting the release of fission products in the fuel.HPR1000 only relies on passive equipment to relieve the core degradation in severe accidents,realize the in-vessel retention of melt,and eliminate the ex-vessel release possibility of fission product.It is hoped that the results can provide references for HPR1000 to formulate the severe accident management guidelines(SAMG).
基金supported by ARO grant W911NF-04-1-0291,NSF grant DMS-0510345 and AFOSR grant FA9550-05-1-0123.
文摘Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms.In this paper,we present a different approach to the same purpose:designing high order well-balanced finite volume weighted essentially non-oscillatory(WENO)schemes and RungeKutta discontinuous Galerkin(RKDG)finite element methods.We make the observation that the traditional RKDG methods are capable of maintaining certain steady states exactly,if a small modification on either the initial condition or the flux is provided.The computational cost to obtain such a well balanced RKDG method is basically the same as the traditional RKDG method.The same idea can be applied to the finite volume WENO schemes.We will first describe the algorithms and prove the well balanced property for the shallow water equations,and then show that the result can be generalized to a class of other balance laws.We perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions,the non-oscillatory property for general solutions with discontinuities,and the genuine high order accuracy in smooth regions.
