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邱建贤: Semi-Lagrangian finite volume WENO scheme for without operator splitting for two-dimensional linear transport equations

时间:2022-11-03来源:数学学院

报告时间:2022年11月4日(星期五)15:00-16:00

报告平台腾讯会议 ID:988 167 036

:邱建贤 教授

工作单位:厦门大学

举办单位:数学学院

报告简介

In this presentation, we present a fourth-order conservative semi-Lagrangian (SL) finite volume (FV) weighted essentially non-oscillatory (WENO) scheme without operator splitting for two-dimensional linear transport equations with applications of kinetic models including the nonlinear Vlasov-Poisson system, the guiding center Vlasov model and the incompressible Euler equation in the vorticity-stream function formulation. To achieve fourth-order accuracy in space, two main ingredients are proposed in the SL FV formulation. Firstly, we introduce a so-called cubic-curved quadrilateral upstream cell and applying an efficient clipping method to evaluate integrals on upstream cells. Secondly, we construct a new WENO reconstruction operator, which recovers a $P^3$ polynomial from neighboring cell averages. Mass conservation is accomplished with the mass conservative nature of the reconstruction operator and the SL formulation. A positivity-preserving limiter is applied to maintain the positivity of the numerical solution wherever appropriate. For nonlinear kinetic models, the SL scheme is coupled with a fourth-order Runge-Kutta exponential integrator for high-order temporal accuracy. Extensive bench marks are tested to verify the designed properties.

报告人简介

邱建贤,厦门大学数学科学学院闽江学者、特聘教授,国际著名刊物 “J. Comp. Phys.” (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和联合基金重点支持项目各一项, 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,获2020年度高等开云平台官网科学研究优秀成果奖(科学技术)--自然科学奖二等奖。多次应邀在国际会议上作大会报告。

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