Deterministic transport on an arbitrarily connected grid
We discuss spatial discretization of the transport equation, concentrating on the problems posed by grids with arbitrary connectivity and arbitrarily-shaped computational cells. We consider both accuracy and efficiency criteria and examine several candidate discretization schemes with respect to these criteria. We show that if arbitrarily-shaped zones are allowed, existing spatial discretization schemes do not provide the desired accuracy in the optically-thick diffusion limit. We present a new scheme that does appear to perform well in the diffusion limit, regardless of the connectivity of the grid or shape of the zones. We show that our new scheme has very nice properties in other limits as well.
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