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An adaptive GRP scheme for compressible fluid flows. (English) Zbl 1329.76205
Summary: This paper presents a second-order accurate adaptive generalized Riemann problem (GRP) scheme for one and two dimensional compressible fluid flows. The current scheme consists of two independent parts: mesh redistribution and PDE evolution. The first part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative interpolation formula is used to calculate the cell-averages and the slopes of conservative variables on the resulting new mesh. The second part is to evolve the compressible fluid flows on a fixed nonuniform mesh with the Eulerian GRP scheme, which is directly extended to two-dimensional arbitrary quadrilateral meshes. Several numerical examples show that the current adaptive GRP scheme does not only improve the resolution as well as accuracy of numerical solutions with a few mesh points, but also reduces possible errors or oscillations effectively.

76M12 Finite volume methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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