题目： RKDG method with conservation constraints and hierarchical reconstruction limiter for solving conservation laws
报告人： Prof Zhiliang Xu, University of Notre Dame, USA
时间：2015.7.2  周三上午， 10:00-11:00
地点：数学楼二楼报告厅
 
Abstract:
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