报告题目：Affine-Invariant WENO Operator on Nonuniform Mesh with Application to Finite Volume and Discontinuous Galerkin Methods

报 告 人：李鹏副教授 石家庄铁道大学

报告摘要：For solving hyperbolic conservation laws that arise frequently in computational physics, high order finite volume WENO (FV-WENO) schemes and discontinuous Galerkin (DG) methods are more popular. However, when there are smaller scale structures in the flow field, the classic FV-WENO schemes will produce a significant oscillation at small scale discontinuities (or large gradients). This phenomenon also exists in DG methods that use nonlinear WENO limiters (DG-WENO), and this will disrupt the stability of numerical methods. In this study, a simple, robust, and effective affine-invariant finite volume WENO (FV-Ai-WENO) scheme under nonuniform meshes is devised. We prove and validate that for any given sensitivity parameter, the WENO operator and the affine transformation operator in the present schemes are commutable. In the presence of smaller scale discontinuities, the new operator satisfies the ENO property while the classic WENO operator does not. In addition, we investigate using FV-Ai-WENO methodology as limiters for the DG methods. Several classical examples are used to verify the performance of the FV-Ai-WENO schemes and DG methods with the Ai-WENO limiter (DG-Ai-WENO) in terms of accuracy, robustness, and affine invariance.

报告人简介：李鹏副教授毕业于北京理工大学爆炸科学与技术国家重点实验室力学专业，目前任教于石家庄铁道大学工程力学系。研究领域为偏微分方程高精度数值方法，主持国家自然科学基金青年项目，河北省自然科学基金面上项目、青年项目，石家庄铁道大学优青项目等，河北省“三三三”第三层次人才，已在SISC、JCP、JSC、ANM等期刊上发表学术论文20余篇。

报告时间：2024年7月12日 9:30-11:00

报告地点：文渊楼 B536

主办单位：数学与统计学院