A novel Local Time Stepping algorithm for shallow water flow simulation in the discontinuous Galerkin framework

Abstract

This paper introduces a generic and efficient Local Time Stepping (LTS) algorithm called Local Flux Flagged-Local Time Stepping (LFF-LTS). The applicability of LFF-LTS algorithm to the solution of shallow water flow equations, utilizing the discontinuous Galerkin finite element framework, is investigated for uniform and non-uniform meshes. The proposed algorithm can be incorporated in any numerical scheme using an explicit time integration scheme. The new scheme is developed by combining and modifying the two existing LTS algorithms, where the domain time step (maximum allowable time step within the domain based on the Courant–Friedrichs–Lewy condition) and the local time step for an element is determined such that the stability criterion is satisfied for all elements. Frozen flux approximation is used during the intermediate time step as the solution for each element is advanced to the domain time step. The algorithm is applied to idealized and practical shallow water flow problems with wet/dry and partially wet bed conditions, and its accuracy and efficiency are compared to the traditional Global Time Stepping (GTS) method. Results show that, with no loss of accuracy, the new LTS algorithm achieves 47–73% CPU time reduction when compared to the GTS method. The accuracy of the LFF-LTS and GTS algorithms are compared with analytical/measured data and found to be in good agreement. The LFF-LTS algorithm is compared with the two existing LTS schemes and found to be more efficient.