COSAM » Events » 2019 » September » DMS Applied Mathematics Smeinat

DMS Applied Mathematics Seminar
Time: Sep 13, 2019 (02:00 PM)
Location: Parker Hall 328

Speaker: T.T. Phuong Hoang (Auburn University)

Title: High Order Explicit Local Time-Stepping Methods For Hyperbolic Conservation Laws

Abstract: We present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta discontinuous Galerkin (RKDG) methods and design LTS algorithms based on the strong stability preserving Runge-Kutta (SSP-RK) schemes that allow spatially variable time step sizes to be used for time integration in different regions of the computational domain. The proposed algorithms are of predictor-corrector type, in which the interface information along the time direction is first predicted based on the SSP-RK approximations and Taylor expansions, and then the fluxes over the region of the interface are corrected to conserve mass exactly at each time step. Following the proposed framework, we derive the corresponding LTS schemes with accuracy up to the fourth order, and prove their conservation property and nonlinear stability for the scalar conservation laws. Numerical results on various test cases are also presented to demonstrate the performance of the proposed LTS algorithms. 

Last updated: 09/09/2019