Multi-level adaptive computations in fluid dynamics

Abstract

The multi-level adaptive technique (MLAT) is a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization. It provides very fast solvers together with adaptive, nearly optimal discretization schemes to general boundary-value problems in general domains. Here the state of the art is surveyed, emphasizing steady-state fluid dynamics applications, from slow viscous flows to transonic ones. Various new techniques are briefly discussed, including distributive relaxation schemes, the treatment of evolution problems, the combined use of upstream and central differencing, local truncation extrapolations, and other 'super-solver' techniques.