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Second-order accurate Godunov scheme for multicomponent flows on moving triangular meshes. (English) Zbl 1220.76047
Summary: This paper presents a second-order accurate adaptive Godunov method for two-dimensional (2D) compressible multicomponent flows, which is an extension of the previous adaptive moving mesh method of H. Tang et al. [SIAM J. Numer. Anal. 41, No. 2, 487–515 (2003; Zbl 1052.65079)] to unstructured triangular meshes in place of the structured quadrangular meshes. The current algorithm solves the governing equations of 2D multicomponent flows and the finite volume approximations of the mesh equations by a fully conservative, second-order accurate Godunov scheme and a relaxed Jacobi-type iteration, respectively. The geometry-based conservative interpolation is employed to remap the solutions from the old mesh to the newly resulting mesh, and a simple slope limiter and a new monitor function are chosen to obtain oscillation-free solutions, and track and resolve both small, local, and large solution gradients automatically. Several numerical experiments are conducted to demonstrate robustness and efficiency of the proposed method. They are a quasi-2D Riemann problem, the double-Mach reflection problem, the forward facing step problem, and two shock wave and bubble interaction problems.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76T30 Three or more component flows
76L05 Shock waves and blast waves in fluid mechanics
Software:
HE-E1GODF
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References:
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