报告时间：2022年11月04日（星期五）15:00-16:00

报告地点：腾讯会议 988167036

报 告 人：邱建贤 教授

工作单位：厦门大学

举办单位：数学与统计学院

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年度高等学校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。