Explicit multi-time stepping methods for convection-dominated flow problems Original Research Article

In this paper we introduce a multi-time stepping method for convection-dominated flow problems. The idea behind this method and its applications will be explained, and the stability and accuracy of the method will be studied by using a one-dimensional model problem: the convection-diffusion equation. Here, the method is applied to a uniform two-block grid. We will prove that local stability conditions in the blocks are sufficient for global stability of the multi-time stepping scheme under certain conditions. Some numerical experiments are performed to investigate cases beyond the theory. We will show that in case of Rung-Kutta-3 time integration extremely large ratios between mesh widths and time steps may be used without affecting the stability of the multi-time stepping method. Conditions for time-accurate behaviour are also investigated by means of numerical experiments.