We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis o...We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.展开更多
The numerical simulation of non conservative system is a difficult challenge for two reasons at least.The first one is that it is not possible to derive jump relations directly from conservation principles,so that in ...The numerical simulation of non conservative system is a difficult challenge for two reasons at least.The first one is that it is not possible to derive jump relations directly from conservation principles,so that in general,if the model description is non ambiguous for smooth solutions,this is no longer the case for discontinuous solutions.From the numerical view point,this leads to the following situation:if a scheme is stable,its limit for mesh convergence will depend on its dissipative structure.This is well known since at least[1].In this paper we are interested in the“dual”problem:given a system in non conservative form and consistent jump relations,how can we construct a numerical scheme that will,for mesh convergence,provide limit solutions that are the exact solution of the problem.In order to investigate this problem,we consider a multiphase flow model for which jump relations are known.Our scheme is an hybridation of Glimm scheme and Roe scheme.展开更多
基金This work was supported by the National Natural Science Foundation of China(No.11472004)the Foundation of Innovation of NUDT(No.B150106).
文摘We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.
基金funded in part by the EU ERC Advanced grant“ADDECCO”#226616This work has been done in part while H.Kumar was a post doc at INRIA,funded by the EU ERC Advanced grant“ADDECCO”#226616.
文摘The numerical simulation of non conservative system is a difficult challenge for two reasons at least.The first one is that it is not possible to derive jump relations directly from conservation principles,so that in general,if the model description is non ambiguous for smooth solutions,this is no longer the case for discontinuous solutions.From the numerical view point,this leads to the following situation:if a scheme is stable,its limit for mesh convergence will depend on its dissipative structure.This is well known since at least[1].In this paper we are interested in the“dual”problem:given a system in non conservative form and consistent jump relations,how can we construct a numerical scheme that will,for mesh convergence,provide limit solutions that are the exact solution of the problem.In order to investigate this problem,we consider a multiphase flow model for which jump relations are known.Our scheme is an hybridation of Glimm scheme and Roe scheme.
