| Popis: |
The simulation of compressible multi-fluid flows receives increasing attention, thanks to extensive engineering applications, but there are still many bottleneck problems remain unresolved due to the presence of singularities (shocks, material interfaces, vortices and other discontinuities etc) in flows, which arises notorious diffculties in all aspects of theoretical justification, numerical analysis and scientific computation. In contrast with single-fluid problems, the treatment of material interfaces become an extremely controversial issue in terms of numerical modeling and numerical methods besides conventional shocks and rarefaction shocks. In this paper this topic is reaccessed and a family of temporal-spatial coupled high order accurate schemes are introduced. The temporal-spatial coupling distinguishes these schemes from the methods of line (e.g. RK-WENO, RK-DG) and implicitly includes many fundamental properties such as thermodynamical consistency, multi-dimensionality and symplecticity. The generalized Riemann solver is adopted to provide high order accurate numerical fluxes and reflect “true” dynamical processes. |
