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The moment-based HWENO with artificial linear weights scheme for hyperbolic conservation laws
报告人:邱建贤教授,厦门大学 时间:2021年4月28日(周三)15:00 字号:

报告地点:行健楼学术活动室526

邀请人:汪艳秋教授

ABSTRACT:In this presentation, we present a fifth-order Hermite weighted essentially non-oscillatory (HWENO) scheme with artificial linear weights for one and two dimensional hyperbolic conser-vation laws, where the zeroth-order and the first-order moments are used in the spatial recon-struction. We construct the HWENO methodology using a nonlinear convex combination of a high degree polynomial with several low degree polynomials, and the associated linear weights can be any artificial positive numbers with only requirement that their summation equals one. The one advantage of the HWENO scheme is its simplicity and easy extension to multi-dimension in engineering applications for we can use any artificial linear weights which are independent on geometry of mesh. The another advantage is its higher order numerical accuracy using less candidate stencils for two dimensional problems. In addition, the HWENO scheme still keeps the compactness as only immediate neighbor information is needed in the reconstruction and has high efficiency for directly using linear approximation in the smooth regions. In order to avoid nonphysical oscillations nearby strong shocks or contact discontinuities, we adopt the thought of limiter for discontinuous Galerkin method to control the spurious oscillations. Some benchmark numerical tests are performed to demonstrate the capability of the proposed scheme.


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