We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity mod...We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.展开更多
In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We u...In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations.Furthermore,we study the interaction between simple waves in detail through exact solution of general initial value problem.Finally,we discuss the all possible interaction of elementary waves using the solution of Riemann problem.展开更多
Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme.The essential feature is that the momentum flux should be of the fo...Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme.The essential feature is that the momentum flux should be of the form ■ are any consistent approximations to the pressure and the mass flux.This scheme thus leaves most terms in the numerical flux unspecified and various authors have used simple averaging.Here we enforce approximate or exact entropy consistency which leads to a unique choice of all the terms in the numerical fluxes.As a consequence novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed.These fluxes are centered and some dissipation has to be added if shocks are present or if the mesh is coarse.We construct scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy condition.Secondly,we use entropy-variable based matrix dissipation flux which leads to kinetic energy and entropy stable schemes.These schemes are shown to be free of entropy violating solutions unlike the original Roe scheme.For hypersonic flows a blended scheme is proposed which gives carbuncle free solutions for blunt body flows.Numerical results for Euler and Navier-Stokes equations are presented to demonstrate the performance of the different schemes.展开更多
文摘We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.
基金Ministry of Human Resource Development,Government of India,for the institute fellowship(grant no.IIT/ACAD/PGS&R/F.II/2/14MA90J08)from IIT KharagpurSERB,DST,India(Ref.No.MTR/2019/001210)for its financial support through MATRICS grant。
文摘In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations.Furthermore,we study the interaction between simple waves in detail through exact solution of general initial value problem.Finally,we discuss the all possible interaction of elementary waves using the solution of Riemann problem.
文摘Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme.The essential feature is that the momentum flux should be of the form ■ are any consistent approximations to the pressure and the mass flux.This scheme thus leaves most terms in the numerical flux unspecified and various authors have used simple averaging.Here we enforce approximate or exact entropy consistency which leads to a unique choice of all the terms in the numerical fluxes.As a consequence novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed.These fluxes are centered and some dissipation has to be added if shocks are present or if the mesh is coarse.We construct scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy condition.Secondly,we use entropy-variable based matrix dissipation flux which leads to kinetic energy and entropy stable schemes.These schemes are shown to be free of entropy violating solutions unlike the original Roe scheme.For hypersonic flows a blended scheme is proposed which gives carbuncle free solutions for blunt body flows.Numerical results for Euler and Navier-Stokes equations are presented to demonstrate the performance of the different schemes.
