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An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of Mathematical Sciences and Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

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NEW APPROACHES OF MUSCL SCHEMES FOR COMPRESSIBLE FLUIDS

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Transactions of Nanjing University of Aeronautics and Astronautics 2001年第Z1期18卷 96-98页

作者： Sung Ik SohnSchool of Information Engineering,Tongmyong University of Information Technology535 Yongdang dong, Pusan 608 711, Korea School of Information Engineering Tongmyong University of Information Technology 535 Yongdang-dong Pusan 608-711 Korea

The MUSCL scheme for compressible gas dynamics is studied in this paper. We propose a new type of Eulerian MUSCL scheme, which evaluates the intercell flux at half time step. The intercell flux is comptuted from characteristic equations with the data which traced back through the approximate characteristic from the edge at half time step. The data is classified in several different types, depending on the characteristic directions of data. We also present a general procedure of oscillation free algorithm for the MUSCL scheme. This procedure provides a class of limiters which includes the existing limiter. The new MUSCL scheme and the oscillation free algorithm are validated through simulations for test problems.

关键词： MUSCL oscillation-free TVD conservation laws

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