Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations (Communications in Computational Physics, 2020)
In this paper, a remapping-free adaptive GRP method for one dimensional(1-D) compressible flows is developed. Based on the framework of finite volumemethod, the 1-D Euler equations are discretized on moving volumes and the resultingnumerical fluxes are computed directly by the GRP method. Thus the remappingprocess in the earlier adaptive GRP algorithm [17,18] is omitted. By adopting a flexiblemoving mesh strategy, this method could be applied for multi-fluid problems. The interfaceof two fluids will be kept at the node of computational grids and the GRP solveris extended at the material interfaces of multi-fluid flows accordingly. Some typical numericaltests show competitive performances of the new method, especially for contactdiscontinuities of one fluid cases and the material interface tracking of multi-fluidcases.