Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true ...Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock locations.However,correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is refined.Here we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee(JWL)equation of state.We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations.Furthermore,we demonstrate that under certain conditions,a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.展开更多
In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the f...In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid.In a numerical scheme,there are many ways that velocity-and stress-continuity can be enforced in the discrete approximation.This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes.The analysis shows that depending on the ratio of densities between the solid and the fluid,some numerical interface conditions are stable up to the maximal CFL-limit,while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit.The paper also presents a new interface condition,obtained as a simplified characteristic boundary condition,that is proved to not suffer from any reduction of the stable CFL-limit.Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.展开更多
基金supported by Lawrence Livermore National Laboratory under the auspices of the U.S.Department of Energy through contract number DE-AC52-07NA27344.
文摘Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities.This is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock locations.However,correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is refined.Here we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee(JWL)equation of state.We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations.Furthermore,we demonstrate that under certain conditions,a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.
基金supported by Lawrence Livermore National Laboratory under the auspices of the U.S.Department of Energy through contract number DE-AC52-07NA27344.
文摘In multi physics computations where a compressible fluid is coupled with a linearly elastic solid,it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid.In a numerical scheme,there are many ways that velocity-and stress-continuity can be enforced in the discrete approximation.This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes.The analysis shows that depending on the ratio of densities between the solid and the fluid,some numerical interface conditions are stable up to the maximal CFL-limit,while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit.The paper also presents a new interface condition,obtained as a simplified characteristic boundary condition,that is proved to not suffer from any reduction of the stable CFL-limit.Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.
