报告题目：RKDG method with conservation constraints and hierarchical reconstruction limiter for solving conservation laws

报告人：Prof. Xu Zhiliang（University of Notre Dame）

报告时间：2015年6月26日周五15:00

报告地点：流体楼C12-619报告厅

主办单位：国际交流合作处、科协、航空宇航学院

We present a new formulation of the Runge�Kutta discontinuous Galerkin (RKDG) method for solving conservation laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. We also present a new hierarchical reconstruction (HR) method  for limiting DG or finite volume solutions up to fourth order of accuracy without local characteristic decomposition on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes.

报告人简介：
许志良教授于1994年和1997年分别获北京航空航天大学机械工程系学士学位和计算机图形学系硕士学位，2002年获美国纽约州立大学石溪分校应用计算数学系博士学位。2003-2006年分别在纽约州立大学石溪分校应用计算数学系和布鲁克黑文国家实验室计算科学中心从事科学研究工作，2006-2010年任教于美国圣母大学数学系，2010年至今任教于圣母大学应用和计算数学系。