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Explicit multi-time stepping methods for convection-dominated flow problems
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DOI：10.1016/S0045-7825(98)80002-9.png)
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Abstract
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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 me 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. (C) 1998 Elsevier Science S.A.
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INTEGRATION
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