Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 217, Issue -, Pages 139-152Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2012.01.002
Keywords
Local time stepping; Multi-rate methods; Shallow water equations; Wetting and drying; Runge-Kutta discontinuous Galerkin methods; Rainfall-runoff
Funding
- National Science Foundation [OCI-0749015]
Ask authors/readers for more resources
Large geophysical flows often encompass both coarse and highly resolved regions. Approximating these flows using shock-capturing methods with explicit time stepping gives rise to a Courant-Friedrichs-Lewy (CFL) time step constraint. Even if the refined regions are sparse, they can restrict the global CFL condition to very small time steps, vastly increasing computational effort over the whole domain. One method to cope with this problem is to use locally varying time steps over the domain. These are also referred to as multi-rate methods in the ODE literature. Ideally, such methods must be conservative, accurate and easy to implement. In this study, we derive a second-order, local time stepping procedure within a Runge-Kutta discontinuous Galerkin (RKDG) framework to solve the shallow water equations. This procedure is based on previous first-order work of the second author and collaborator Kirby [1-3]. As we are interested in both coastal and overland flows due to, e.g., rainfall, wetting and drying is incorporated into the model. Numerical results are shown, which verify the accuracy and efficiency of the approach (compared to using a globally defined CFL time step), and the application of the method to rainfall-runoff scenarios. Published by Elsevier B.V.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available