Logo

A Conservative Semi-Lagrangian Hybrid Hermite WENO Scheme for Linear Transport Equations and the Nonlinear Vlasov-Poisson System

Ab94890f7f13d568b275e213fbf827f2cd1e027e

Speaker

Jianxian Qiu, Xiamen University

Time

2020.10.28 10:00-11:00

Venue

Online—ZOOM APP

ZOOM Info

ZOOM Link
Conference ID: 965-438-75439
PIN Code: 541624

Abstract

In this presentation, we will present a high order conservative semi-Lagrangian (SL) hybrid Hermite weighted essentially non-oscillatory (HWENO) scheme for linear transport equations and the nonlinear Vlasov-Poisson (VP) system. The proposed SL hybrid HWENO scheme adopts a weak formulation of the characteristic Galerkin method and introduces an adjoint problem for the test function in the same way as the SL discontinuous Galerkin (DG) scheme {Guo et al, Monthly Weather Review, 142 (2014), pp. 457-475.}. Comparing with the original SL DG scheme, we introduce a hybrid moment-based (MB) HWENO reconstruction operator in space, bringing at least two benefits. Firstly, with the same order of accuracy, such a reconstruction allows less degrees of freedom per element in the evolution process. Secondly, it naturally possesses a nonoscillatory property when dealing with discontinuity. In addition, we derive a novel troubled cell indicator which can effectively detect the discontinuous regions for the reconstruction operator. To apply the scheme for 2-D transport equations and the nonlinear VP system, we adopt a fourthorder dimensional splitting method. Positivity-preserving (PP) limiters are applied to enforce the positivity of the solution for the system having positive solutions. Finally, we show extensive numerical tests to validate the effectiveness of the proposed SL hybrid WENO scheme.

Bio

邱建贤,厦门大学数学科学学院教授,博士生导师,国际著名刊物“Journal of Computational Physics” (计算物理) 编委,中国计算数学学会常务理事。 主要从事流体力学的数值方法和偏微分方程数值解的研究工作,重点研究对流占优问题的数值方法,包括间断Galerkin (DG) 有限元方法 、有限差分方法及有限体积法中的本质无振荡(ENO)、加权ENO (WENO)方法,以及这些方法在计算流体力学中的应用。

Sponsors