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Remapping-free adaptive GRP method for multi-fluid flows I: One dimensional Euler equations. (English) Zbl 1373.76142
Summary: In this paper, a remapping-free adaptive GRP method for one dimensional (1-D) compressible flows is developed. Based on the framework of finite volume method, the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP method. Thus the remapping process in the earlier adaptive GRP algorithm [E. Han et al., J. Comput. Phys. 229, No. 5, 1448–1466 (2010; Zbl 1329.76205); Commun. Comput. Phys. 10, No. 3, 577–609 (2011; Zbl 1373.76130)] is omitted. By adopting a flexible moving mesh strategy, this method could be applied for multi-fluid problems. The interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows accordingly. Some typical numerical tests show competitive performances of the new method, especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
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