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APPLICATION OF RICHARDSON EXTRAPOLATION WITH THE CRANK – NICOLSON SCHEME FOR MULTI-DIMENSIONAL ADVECTION

Multi-dimensional advection terms are an important part of many large-scale mathematical models which arise in different fields of science and engineering. After applying some kind of splitting, these terms can be handled separately from the remaining part of the mathematical model under consideration. It is important to treat the multi-dimensional advection in a sufficiently accurate manner. It is shown in this paper that high order of accuracy can be achieved when the well-known Crank– Nicolson numerical scheme is combined with the Richardson extrapolation. 1. Multi-dimensional advection equations Consider the multi-dimensional advection equation: