Multigrid techniques as applied to gasdynamic simulation on unstructured meshes

A multigrid method is proposed for solving the system of difference equations obtained via the finite-volume discretization of the Euler or Navier–Stokes equations on an unstructured mesh. A sequence of nested unstructured grids is generated via collapsing faces that take into account the features of the problem (inviscid/viscous). The capabilities of the approach are demonstrated by computing inviscid and viscous compressible uniform flows around an airfoil on structured, unstructured, and hybrid meshes. The topology of grids of different levels is described. Their quality and the influence of the grid structure on the convergence factor of the multigrid method are discussed.