Integration of a shallow water model with a local time step

Abstract

A Local Time Stepping (LTS) scheme was applied to an explicit Godunov–type shallow–water model to improve run–time efficiency. Using LTS, the solution in each cell is advanced with the largest power of two multiple of the global time step required for stability, δt, that satisfies the local criterion for stability.A careful sequencing of flux calculations and solution updates ensures conservation. Test problems including practical applications show that LTS achieves run–time reductions ranging from 50 to 70% without loss of accuracy. In addition, a four level scheme that coordinates time steps of δt, 2δt, 4δt, and 8δt performs best in idealized and practical test problems considered for this study. Additional levels achieve no further reduction in run time, and in some cases cause instability and deteriorate conservation.

Keywords:

• Dam-break
• finite volume
• flood modeling
• local time stepping
• shallow-water equations