报告题目：A conservative semi-Lagrangian HWENO scheme for linear transport equations

报告时间：2021年6月18日，星期五，下午16:30-17:30

报告地点：数学楼2-3会议室

报告人：邱建贤教授，厦门大学数学学院

报告摘要：

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 non[1]oscillatory 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 fourth[1]order 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 HWENO scheme.

报告人简介：

    邱建贤教授为厦门大学闽江学者特聘教授，福建省数学建模与高性能计算重点实验室常务副主任，中国计算数学学会常务理事，福建省数学学会常务理事，入选福建省第四批“百人计划”，国际权威刊物 Journal of Computational Physics 编委。1982年获得中国地质大学（武汉）学士学位，1988年获得南京航空航天大学硕士学位，2001年获得南京航空航天大学博士学位。主要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，已发表论文七十多篇，多次受邀在国际会议上作大会报告。