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Second-Order Accurate Godunov Scheme for Multicomponent Flows on Moving Triangular Meshes

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Abstract

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 Tang et al. (SIAM J. Numer. Anal. 41:487–515, 2003) 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.

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Correspondence to Huazhong Tang.

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Chen, G., Tang, H. & Zhang, P. Second-Order Accurate Godunov Scheme for Multicomponent Flows on Moving Triangular Meshes. J Sci Comput 34, 64–86 (2008). https://doi.org/10.1007/s10915-007-9162-8

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  • DOI: https://doi.org/10.1007/s10915-007-9162-8

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