High order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter

题目：High order schemes for conservation laws on arbitrarily distributed point clouds with a simple WENO limiter

时间：1月4日 下午15:00―17:00

地点：工商楼200-9

报告人:杜洁

杜洁，清华大学丘成桐数学科学中心助理教授。2015年获得中国科学技术大学理学博士学位。2015.08-2017.08为香港中文大学数学系博士后。2017年9月入职清华大学。杜洁的研究领域为偏微分方程数值解。主要科研兴趣为DG、WENO、CPR等数值算法，以及交通流问题的建模和数值模拟。

摘要：In this talk, I will show a high order stable method for solving hyperbolic conservation laws on arbitrarily distributed point clouds. An algorithm of building a suitable polygonal mesh based on the random points is given and the traditional discontinuous Galerkin (DG) method is adopted on the constructed polygonal mesh. We also adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for DG schemes on two-dimensional unstructured triangular meshes, to our high order method on polygonal meshes. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the original method in smooth regions and control spurious numerical oscillations near discontinuities. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good behavior of our method.

联系人：仲杏慧老师（zhongxh@zju.edu.cn）