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A 5th order monotonicity-preserving upwind compact difference scheme

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Abstract

Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme (m-UCD5) is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By employing the component-wise and characteristic-wise methods, two forms of the new difference scheme are proposed to solve the N-S/Euler equation. Through the Sod problem, the Shu-Osher problem and the two-dimensional Double Mach Reflection problem, numerical solutions have demonstrated this new scheme does have a good resolution of high wave number and a robust ability of capturing shock waves, leading to a conclusion that the new difference scheme may be used to simulate complex flows containing shock waves.

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Authors and Affiliations

  1. The Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    ZhiWei He & XinLiang Li

  2. The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    DeXun Fu & YanWen Ma

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  1. ZhiWei He
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  2. XinLiang Li
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  3. DeXun Fu
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  4. YanWen Ma
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Correspondence to XinLiang Li.

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He, Z., Li, X., Fu, D. et al. A 5th order monotonicity-preserving upwind compact difference scheme. Sci. China Phys. Mech. Astron. 54, 511–522 (2011). https://doi.org/10.1007/s11433-010-4220-x

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  • DOI: https://doi.org/10.1007/s11433-010-4220-x

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