Speaker: Mr. Nanyi Zheng (郑南艺）

Time: 12:10-13:10, 1 September 2022 (Thursday) (Beijing time)

Tencent Meeting ID: 619-677-055

Venue: C404, Lijiao Building

Abstract

In this report, a fourth-order conservative semi-Lagrangian (SL) finite volume (FV) weighted essentially non-oscillatory (WENO) scheme without operator splitting is presented 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 P3 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.

About Mr. Zheng

Mr. Nanyi Zheng is a PhD candidate in School of Mathematical Sciences Xiamen University. His research interest focuses mainly on developing high-order semi-Lagrangian/Eulerian-Lagrangian schemes for kinetic and fluid dynamics.