As seen in previous chapters, the last two decades have witnessed the appearance of a number of numerical techniques to handle problems with complex geometries and/or moving bodies. The main elements of any comprehensive capability to solve this class of problems are:

  • automatic grid generation;
  • solvers for moving grids/boundaries; and
  • treatment of grids surrounding moving bodies.

Three leading techniques to resolve problems of this kind are as follows.

  • Solvers based on unstructured, moving (ALE) grids. These guarantee conservation, a smooth variation of grid size, but incur extra costs due to mesh movement/smoothing techniques and remeshing, and may have locally reduced accuracy due to distorted elements; for some examples, see Löhner (1990), Baum et al. (1995b), Löhner et al. (1999b) and Sharov et al. (2000).
  • Solvers based on overlapping grids. These do not require any remeshing, can use fast mesh movement techniques, allow for independent component/body gridding, but suffer from loss of conservation, incur extra costs due to interpolation and may have locally reduced accuracy due to drastic grid size variation; for some examples, see Steger et al. (1983), Benek et al. (1985), Buning et al. (1988), Dougherty and Kuan (1989), Meakin and Suhs (1989), Meakin (1993), Nirschl et al. (1994), Meakin (1997), Rogers et al. (1998) and Regnström et al. (2000), Togashi et al. (2000), Löhner (2001), Togashi et al. (2006a,b).
  • Solvers based on adaptive embedded grids ...

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