報告題目：The moment-based HWENO with artificial linear weights scheme for hyperbolic conservation laws
報 告 人：邱建賢 教授 廈門大學數學科學學院
報告時間：2021年5月6日 14:00-15:00
報告地點：伟德线上平台三樓會議室
校内聯系人：陶詹晶 zjtao@jlu.edu.cn
報告摘要：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 conservation laws, where the zeroth-order and the first-order moments are used in the spatial reconstruction. 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. 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.
報告人簡介：邱建賢，廈門大學數學科學學院教授，國際著名刊物 “J. Comp. Phys.” (計算物理) 編委。從事計算流體力學及微分方程數值解法的研究工作，在間斷Galerkin（DG）、加權本質無振蕩（WENO）數值方法的研究及其應用方面取得了一些重要成果，已發表論文一百多篇。主持國家自然科學基金重點項目和聯合基金重點支持項目各一項, 參與歐盟第六框架特别研究項目, 是項目組中唯一非歐盟的成員。獲教育部自然科學獎二等獎，多次被邀請在國際會議上作大會報告。
