An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density...An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.展开更多
The concept of diffusion regulation(DR)was originally proposed by Jaisankar for traditional second order finite volume Euler solvers.This was used to decrease the inherent dissipation associated with using approximate...The concept of diffusion regulation(DR)was originally proposed by Jaisankar for traditional second order finite volume Euler solvers.This was used to decrease the inherent dissipation associated with using approximate Riemann solvers.In this paper,the above concept is extended to the high order spectral volume(SV)method.The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms.Numerical experiments were conducted to compare and contrast the original and the DR formulations.These experiments demonstrated(i)retention of high order accuracy for the new formulation,(ii)higher fidelity of the DR formulation,when compared to the original scheme for all orders and(iii)straightforward extension to Navier Stokes equations,since the DR does not interfere with the discretization of the viscous fluxes.In general,the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.展开更多
基金supported by the French"Commissariat´a l’Energie Atomique(CEA)"(Centre de Saclay)in the frame of the contract"ASTRE",#SAV 34160the Marie Curie Actions of the European Commission in the frame of the DEASE project(MESTCT-2005-021122)。
文摘An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.
基金The first author gratefully acknowledges and appreciates the discussions he had with Prof.Raghurama Rao and Dr.Jaisankar,Indian Institute of Science,Bangalore,India.
文摘The concept of diffusion regulation(DR)was originally proposed by Jaisankar for traditional second order finite volume Euler solvers.This was used to decrease the inherent dissipation associated with using approximate Riemann solvers.In this paper,the above concept is extended to the high order spectral volume(SV)method.The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms.Numerical experiments were conducted to compare and contrast the original and the DR formulations.These experiments demonstrated(i)retention of high order accuracy for the new formulation,(ii)higher fidelity of the DR formulation,when compared to the original scheme for all orders and(iii)straightforward extension to Navier Stokes equations,since the DR does not interfere with the discretization of the viscous fluxes.In general,the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.
