Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Method for nonlinear Vlasov models
报告摘要：Semi-Lagrangian (SL) approach is attractive in transport simulations, e.g. in climate modeling and kinetic models, due to its numerical stability in allowing extra-large time-stepping sizes. For practical problems with complex geometry, schemes on the unstructured meshes are preferred. However, accurate and mass conservative SL methods on unstructured meshes are still under development and encounter several challenges. For instance, when tracking characteristics backward in time, high order curves are required to accurately approximate the shape of upstream cells, which brings in extra computational complexity. To avoid such computational complexity, we propose an Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method with discussion on the treatment of inflow boundary condition. The nonlinear WENO limiter is applied to control oscillations. Desired properties of the proposed method are numerically verified by a set of benchmarks tests.
个人简介：蔡晓峰博士，北京师范大学珠海校区和北师港浸大助理教授，2016年博士毕业于厦门大学，随后在休斯敦大学和特拉华大学做博士后研究，研究工作主要面向等离子体物理模拟、数值天气预报等领域，针对相应的复杂流体力学方程等偏微分方程和问题，致力于发展高效稳健可靠的高阶数值方法。主持国家自然科学基金青年项目。在SIAM Journal on Scientific Computing、Journal of Computational Physics、Mathematics of Computation、Computer Methods in Applied Mechanics and Engineering等权威期刊上发表20篇论文。