报告题目: An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

报告时间：2023年9月4日（周一）上午10:30-12:00

报告地点：数学楼2-3会议室

报告摘要: In this presentation, we introduce a sixth order oscillation-free Hermite weighted essentially non-oscillatory (OF-HWENO) scheme for hyperbolic conservation laws on structured meshes, where the zeroth- and first-order moments are the variables for the governing equations. The main difference from other HWENO schemes existed in the literature is that we add high order numerical damping terms in the first-order moment equations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only can achieve the designed optimal numerical order, but also easily be implemented for we use only one set of stencil in reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- and first-order moments equations. In order to obtain adaptive order resolution when facing the discontinuities, a transition polynomial is added in the reconstruction, where the associated linear weights can also be any positive numbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps the compactness as only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests are performed to illustrate the high order accuracy, high resolution and robustness of the proposed scheme.

报告人简介：邱建贤，厦门大学数学科学学院教授，国际著名刊物“Journal of Computational Physics” (计算物理) 编委。从事计算流体力学及微分方程数值解法的研究工作，在间断Galerkin（DG）、加权本质无振荡（WENO）数值方法的研究及其应用方面取得了一些重要成果，已发表论文一百多篇。主持国家自然科学基金重点项目、联合基金重点支持项目和国家重点研发项目之课题各一项, 参与欧盟第六框架特别研究项目, 是项目组中唯一非欧盟的成员，多次应邀在国际会议上作大会报告。获2020年度教育部自然科学奖二等奖，2021年度福建省自然科学奖二等奖各一项。

邀请人：令丹