A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding cr...A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）展开更多
Since proposed,the self-similarity variables based genuinely multidimensional Riemann solver is attracting more attentions due to its high resolution in multidimensional complex flows.However,it needs numerous logical...Since proposed,the self-similarity variables based genuinely multidimensional Riemann solver is attracting more attentions due to its high resolution in multidimensional complex flows.However,it needs numerous logical operations in supersonic cases,which limit the method’s applicability in engineering problems greatly.In order to overcome this defect,a hybrid multidimensional Riemann solver,called HMTHS(Hybrid of MulTv and multidimensional HLL scheme based on Self-similar structures),is proposed.It simulates the strongly interacting zone by adopting the MHLLES(Multidimensional Harten-Lax-van Leer-Eifeldt scheme based on Self-similar structures)scheme at subsonic speeds,which is with a high resolution by considering the second moment in the similarity variables.Also,it adopts the MULTV(Multidimensional Toro and Vasquez)scheme,which is with a high resolution in capturing discontinuities,to simulate the flux at supersonic speeds.Systematic numerical experiments,including both one-dimensional cases and twodimensional cases,are conducted.One-dimensional moving contact discontinuity case and sod shock tube case suggest that HMTHS can accurately capture one-dimensional expansion waves,shock waves,and linear contact discontinuities.Two-dimensional cases,such as the double Mach reflection case,the supersonic shock/boundary layer interaction case,the hypersonic flow over the cylinder case,and the hypersonic viscous flow over the double-ellipsoid case,indicate that the HMTHS scheme is with a high resolution in simulating multidimensional complex flows.Therefore,it is promising to be widely applied in both scholar and engineering areas.展开更多
By applying the least squares solution for the middle wave analysis inside the Riemann fan,we construct a four-state Harten-Lax-van Leer(HLL)Riemann solver for numerical simulation of magneto-hydrodynamics(MHD).First,...By applying the least squares solution for the middle wave analysis inside the Riemann fan,we construct a four-state Harten-Lax-van Leer(HLL)Riemann solver for numerical simulation of magneto-hydrodynamics(MHD).First,we revisit the twostate HLL scheme and obtain the two outer intermediate states across the two outbounding fast waves through Rankine-Hugoniot(R-H)conditions;Second,the two inner intermediate states are calculated using a geometric interpretation of the R-H conditions across the middle contact wave.This newly constructed four-state HLL solver contains different wave structures from those of the HLLD Riemann solver;namely,the two Alfv´en waves are replaced as the two combination waves originated from the merging of Alfv´en and slow waves inside the Riemann fan.As we tested,this solver resolves the MHD discontinuities well,and has better capture ability than the HLLD solver for the slow waves,although it appears more diffusive than the latter in the situations where the slow waves are not solely generated.Overall,the new solver has the similar accuracy as the HLLD solver,thus it is suitable for the calculation of numerical fluxes for the Godunov-type numerical simulation ofMHDequations where the slow waves are expected to be resolved.展开更多
Combining robustness and high accuracy is one of the primary challenges in the magnetohydrodynamics(MHD)field of numerical methods.This paper investigates two critical physical constraints:wave order and positivity-pr...Combining robustness and high accuracy is one of the primary challenges in the magnetohydrodynamics(MHD)field of numerical methods.This paper investigates two critical physical constraints:wave order and positivity-preserving(PP)properties of the high-resolution HLLD Riemann solver,which ensures the positivity of density,pressure,and internal energy.This method’s distinctiveness lies in its ability to ensure that the wave characteristic speeds of the HLLD Riemann solver are strictly ordered.A provably PP HLLD Riemann solver based on the Lagrangian setting is established,which can be viewed as an extension of the PP Lagrangianmethod in hydrodynamics but with more and stronger constraint condition.In addition,the above two properties are ensured on moving grid method by employing the Lagrange-to-Euler transform.Meanwhile,a novel multi-moment constrained finite volume method is introduced to acquire third order accuracy,and practical limiters are applied to avoid numerical oscillations.Selected numerical benchmarks demonstrate the robustness and accuracy of our methods.展开更多
The aim of the present work is to develop a general formalism to derive staggered discretizations for Lagrangian hydrodynamics on two-dimensional unstructured grids.To this end,we make use of the compatible discretiza...The aim of the present work is to develop a general formalism to derive staggered discretizations for Lagrangian hydrodynamics on two-dimensional unstructured grids.To this end,we make use of the compatible discretization that has been initially introduced by E.J.Caramana et al.,in J.Comput.Phys.,146(1998).Namely,momentum equation is discretized by means of subcell forces and specific internal energy equation is obtained using total energy conservation.The main contribution of this work lies in the fact that the subcell force is derived invoking Galilean invariance and thermodynamic consistency.That is,we deduce a general form of the sub-cell force so that a cell entropy inequality is satisfied.The subcell force writes as a pressure contribution plus a tensorial viscous contribution which is proportional to the difference between the nodal velocity and the cell-centered velocity.This cell-centered velocity is a supplementary degree of freedom that is solved by means of a cell-centered approximate Riemann solver.To satisfy the second law of thermodynamics,the local subcell tensor involved in the viscous part of the subcell force must be symmetric positive definite.This subcell tensor is the cornerstone of the scheme.One particular expression of this tensor is given.A high-order extension of this discretization is provided.Numerical tests are presented in order to assess the efficiency of this approach.The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of this scheme.展开更多
In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire＇s requirement, to the Maire＇s node-based Lagrangian scheme developed in [P. H. Maire et al., SIAM J. Sci. Comput, 29 （2007）, 1781-...In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire＇s requirement, to the Maire＇s node-based Lagrangian scheme developed in [P. H. Maire et al., SIAM J. Sci. Comput, 29 （2007）, 1781-1824]. In particular, we apply the so-called Multi-Fluid Channel on Averaged Volume （MFCAV） Riemann solver and a Riemann solver that adaptively combines the MFCAV solver with other more dissipative Riemann solvers to the Maire＇s scheme. It is noted that neither of the two solvers satisfies the Maire＇s requirement. Numerical experiments are presented to demonstrate that the application of the two Riemann solvers is successful.展开更多
This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which ca...This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.展开更多
We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between...We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between the fluid and solid in the case of phase transitions.The hydrostatic components of the solid is described by a family of general Mie-Gruneisen equation of state(EOS),while the deviatoric component includes the elastic phase,linearly hardened plastic phase and fluid phase.The approximate solver provides the interface stress and normal velocity by an iterative method.The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state.The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds.Several numerical examples,including Riemann problems,shock-bubble interactions,implosions and high speed impact applications,are presented to validate the approximate solver.展开更多
In this work,a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow.To consider the effects of wave interaction from both the x-and y-directions,a corresponding 2D el...In this work,a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow.To consider the effects of wave interaction from both the x-and y-directions,a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded.The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region.The stress is updated separately by using the velocity obtained with the above approximate Riemann solver.Several numerical tests,including genuinely two-dimensional examples,are presented to test the performances of the proposed method.The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.展开更多
This paper summarizes a Riemann-solver-free spacetime discontinuous Galerkin method developed for general conservation laws. The method integrates the best features of the spacetime Conservation Element/Solution Eleme...This paper summarizes a Riemann-solver-free spacetime discontinuous Galerkin method developed for general conservation laws. The method integrates the best features of the spacetime Conservation Element/Solution Element (CE/SE) method and the discontinuous Galerkin (DG) method. The core idea is to construct a staggered spacetime mesh through alternate cell-centered CEs and vertex-centered CEs within each time step. Inside each SE, the solution is approximated using high-order spacetime DG basis polynomials. The spacetime flux conservation is enforced inside each CE using the DG concept. The unknowns are stored at both vertices and cell centroids of the spatial mesh. However, the solutions at vertices and cell centroids are updated at different time levels within each time step in an alternate fashion. Thanks to the staggered spacetime formulation, there are no left and right states for the solution at the spacetime interface. Instead, the solution available to evaluate the flux is continuous across the interface. Therefore, no (approximate) Riemann solvers are needed to provide a unique numerical flux. The current method can be used to solve arbitrary conservation laws including the compressible Euler equations, shallow water equations and magnetohydrodynamics (MHD) equations without the need of any form of Riemann solvers. A set of benchmark problems of various conservation laws are presented to demonstrate the accuracy of the method.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11172050 and11672047)the Science and Technology Foundation of China Academy of Engineering Physics(No.2013A0202011)
文摘A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）
基金This study was co-supported by National Natural Science Foundation of China(Nos.11902265 and 11972308)Natural Science Foundation of Shaanxi Province of China(No.2019JQ-376)the Fundamental Research Funds for the Central Universities of China(Nos.G2018KY0304 and G2018KY0308).
文摘Since proposed,the self-similarity variables based genuinely multidimensional Riemann solver is attracting more attentions due to its high resolution in multidimensional complex flows.However,it needs numerous logical operations in supersonic cases,which limit the method’s applicability in engineering problems greatly.In order to overcome this defect,a hybrid multidimensional Riemann solver,called HMTHS(Hybrid of MulTv and multidimensional HLL scheme based on Self-similar structures),is proposed.It simulates the strongly interacting zone by adopting the MHLLES(Multidimensional Harten-Lax-van Leer-Eifeldt scheme based on Self-similar structures)scheme at subsonic speeds,which is with a high resolution by considering the second moment in the similarity variables.Also,it adopts the MULTV(Multidimensional Toro and Vasquez)scheme,which is with a high resolution in capturing discontinuities,to simulate the flux at supersonic speeds.Systematic numerical experiments,including both one-dimensional cases and twodimensional cases,are conducted.One-dimensional moving contact discontinuity case and sod shock tube case suggest that HMTHS can accurately capture one-dimensional expansion waves,shock waves,and linear contact discontinuities.Two-dimensional cases,such as the double Mach reflection case,the supersonic shock/boundary layer interaction case,the hypersonic flow over the cylinder case,and the hypersonic viscous flow over the double-ellipsoid case,indicate that the HMTHS scheme is with a high resolution in simulating multidimensional complex flows.Therefore,it is promising to be widely applied in both scholar and engineering areas.
基金supported by NNSFC grants 42150105 and 42188101National Key R&D program of China No.2021YFA0718600the Pandeng Program of National Space Science Center,Chinese Academy of Sciences.
文摘By applying the least squares solution for the middle wave analysis inside the Riemann fan,we construct a four-state Harten-Lax-van Leer(HLL)Riemann solver for numerical simulation of magneto-hydrodynamics(MHD).First,we revisit the twostate HLL scheme and obtain the two outer intermediate states across the two outbounding fast waves through Rankine-Hugoniot(R-H)conditions;Second,the two inner intermediate states are calculated using a geometric interpretation of the R-H conditions across the middle contact wave.This newly constructed four-state HLL solver contains different wave structures from those of the HLLD Riemann solver;namely,the two Alfv´en waves are replaced as the two combination waves originated from the merging of Alfv´en and slow waves inside the Riemann fan.As we tested,this solver resolves the MHD discontinuities well,and has better capture ability than the HLLD solver for the slow waves,although it appears more diffusive than the latter in the situations where the slow waves are not solely generated.Overall,the new solver has the similar accuracy as the HLLD solver,thus it is suitable for the calculation of numerical fluxes for the Godunov-type numerical simulation ofMHDequations where the slow waves are expected to be resolved.
基金supported by the National Natural Science Foundation of China(12131002,11971071,12288101)Foundation of National Key Laboratory of Computational Physics(6142A05220201)China Postdoctoral Science Foundation(2024M760059).
文摘Combining robustness and high accuracy is one of the primary challenges in the magnetohydrodynamics(MHD)field of numerical methods.This paper investigates two critical physical constraints:wave order and positivity-preserving(PP)properties of the high-resolution HLLD Riemann solver,which ensures the positivity of density,pressure,and internal energy.This method’s distinctiveness lies in its ability to ensure that the wave characteristic speeds of the HLLD Riemann solver are strictly ordered.A provably PP HLLD Riemann solver based on the Lagrangian setting is established,which can be viewed as an extension of the PP Lagrangianmethod in hydrodynamics but with more and stronger constraint condition.In addition,the above two properties are ensured on moving grid method by employing the Lagrange-to-Euler transform.Meanwhile,a novel multi-moment constrained finite volume method is introduced to acquire third order accuracy,and practical limiters are applied to avoid numerical oscillations.Selected numerical benchmarks demonstrate the robustness and accuracy of our methods.
基金supported by the Czech Ministry of Education grants MSM 6840770022,MSM 6840770010,LC528the Czech Science Foundation grant P205/10/0814.
文摘The aim of the present work is to develop a general formalism to derive staggered discretizations for Lagrangian hydrodynamics on two-dimensional unstructured grids.To this end,we make use of the compatible discretization that has been initially introduced by E.J.Caramana et al.,in J.Comput.Phys.,146(1998).Namely,momentum equation is discretized by means of subcell forces and specific internal energy equation is obtained using total energy conservation.The main contribution of this work lies in the fact that the subcell force is derived invoking Galilean invariance and thermodynamic consistency.That is,we deduce a general form of the sub-cell force so that a cell entropy inequality is satisfied.The subcell force writes as a pressure contribution plus a tensorial viscous contribution which is proportional to the difference between the nodal velocity and the cell-centered velocity.This cell-centered velocity is a supplementary degree of freedom that is solved by means of a cell-centered approximate Riemann solver.To satisfy the second law of thermodynamics,the local subcell tensor involved in the viscous part of the subcell force must be symmetric positive definite.This subcell tensor is the cornerstone of the scheme.One particular expression of this tensor is given.A high-order extension of this discretization is provided.Numerical tests are presented in order to assess the efficiency of this approach.The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of this scheme.
文摘In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire＇s requirement, to the Maire＇s node-based Lagrangian scheme developed in [P. H. Maire et al., SIAM J. Sci. Comput, 29 （2007）, 1781-1824]. In particular, we apply the so-called Multi-Fluid Channel on Averaged Volume （MFCAV） Riemann solver and a Riemann solver that adaptively combines the MFCAV solver with other more dissipative Riemann solvers to the Maire＇s scheme. It is noted that neither of the two solvers satisfies the Maire＇s requirement. Numerical experiments are presented to demonstrate that the application of the two Riemann solvers is successful.
基金Project supported by the National Natural Science Foundation of China(U1630249,11971071,11971069,11871113)the Science Challenge Project(JCKY2016212A502)the Foundation of Laboratory of Computation Physics.
文摘This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.
基金supports provided by the National Natural Science Foundation of China(Grant Nos.91630310,11421110001,and 11421101)and Science Challenge Project(No.TZ 2016002).
文摘We propose a robust approximate solver for the hydro-elastoplastic solid material,a general constitutive law extensively applied in explosion and high speed impact dynamics,and provide a natural transformation between the fluid and solid in the case of phase transitions.The hydrostatic components of the solid is described by a family of general Mie-Gruneisen equation of state(EOS),while the deviatoric component includes the elastic phase,linearly hardened plastic phase and fluid phase.The approximate solver provides the interface stress and normal velocity by an iterative method.The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state.The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds.Several numerical examples,including Riemann problems,shock-bubble interactions,implosions and high speed impact applications,are presented to validate the approximate solver.
基金supported by the NSFC-NSAF joint fund(Grant No.U1730118)the Science Challenge Project(Grant No.JCKY2016212A502)+1 种基金the National Natural Science Foundation of China(Grant No.12101029)Postdoctoral Science Foundation of China(Grant No.2020M680283).
文摘In this work,a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow.To consider the effects of wave interaction from both the x-and y-directions,a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded.The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region.The stress is updated separately by using the velocity obtained with the above approximate Riemann solver.Several numerical tests,including genuinely two-dimensional examples,are presented to test the performances of the proposed method.The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.
文摘This paper summarizes a Riemann-solver-free spacetime discontinuous Galerkin method developed for general conservation laws. The method integrates the best features of the spacetime Conservation Element/Solution Element (CE/SE) method and the discontinuous Galerkin (DG) method. The core idea is to construct a staggered spacetime mesh through alternate cell-centered CEs and vertex-centered CEs within each time step. Inside each SE, the solution is approximated using high-order spacetime DG basis polynomials. The spacetime flux conservation is enforced inside each CE using the DG concept. The unknowns are stored at both vertices and cell centroids of the spatial mesh. However, the solutions at vertices and cell centroids are updated at different time levels within each time step in an alternate fashion. Thanks to the staggered spacetime formulation, there are no left and right states for the solution at the spacetime interface. Instead, the solution available to evaluate the flux is continuous across the interface. Therefore, no (approximate) Riemann solvers are needed to provide a unique numerical flux. The current method can be used to solve arbitrary conservation laws including the compressible Euler equations, shallow water equations and magnetohydrodynamics (MHD) equations without the need of any form of Riemann solvers. A set of benchmark problems of various conservation laws are presented to demonstrate the accuracy of the method.
