Scientific Computing Group Seminars - Detail View

Speaker: J. Qiu

Affiliation: Nanjing University, China

Talk Title: Adaptive Runge-Kutta discontinuous Galerkin methods with different indicators

Invited by: Chi-Wang Shu

Time: Oct. 10 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

In this presentation , we systematically investigate adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators which were based on the troubled cell indicators studied by Qiu and Shu [SIAM J. Sci. Comput., 27 (2005), 995-1013], with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. Both $h$-version and $r$-version adaptive methods are considered in the paper. The idea is to first identify ``troubled cells'' by different troubled-cell indicators, namely those cells where limiting might be needed and discontinuities might appear, then adopt an adaptive approach in these cells. A detailed numerical study in one dimensional case is performed, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.