Body capturing using adaptive cartesian grids
S. A. E. G. Falle, J. R. Giddings · 1994
Abstract In recent years there has been considerable interest in using adaptive cartesian grids to compute complex flows (e.g. Berger & Collela 1989; Berger & Leveque 1990; Quirk, J.J. 1990). Such methods are extremely effective for the interior part of the flow, but they suffer from the disadvantage that they do not represent solid surfaces as accurately as body fitted grids. This difficulty can in part be overcome by using a polygonal representation of the body surface (Leveque 1988, Quirk 1992), but it is then impossible to avoid the presence of extremely small cells which lead to very small time steps when using explicit schemes. For inviscid problems this time step restriction can be avoided by allowing waves to pass through more than one cell in a time step (Leveque 1988, Berger & Leveque 1990), merging the small cells with neighbouring large ones (Quirk 1992) or using sub time stepping in the small cells. However, it is not easy to extend these ideas to viscous problems or to more than two dimensions, and it is therefore worth exploring alternative approaches.