報告題目：RKDG method with conservation constraints and hierarchical reconstruction limiter for solving conservation laws

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

報告時間：2015年6月26日周五15:00

報告地點：流體樓C12-619報告廳

主辦單位：國際交流合作處、科協、航空宇航學院

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.

報告人簡介：
許志良教授于1994年和1997年分别獲北京航空航天大學機械工程系學士學位和計算機圖形學系碩士學位，2002年獲美國紐約州立大學石溪分校應用計算數學系博士學位。2003-2006年分别在紐約州立大學石溪分校應用計算數學系和布魯克黑文國家實驗室計算科學中心從事科學研究工作，2006-2010年任教于美國聖母大學數學系，2010年至今任教于聖母大學應用和計算數學系。