Three-dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations

A solution adaptive multigrid scheme for solving the three-dimensional Navier-Stokes equations on unstructured meshes is presented. The algorithm solves the equations on a fully unstructured mesh of tetrahedral elements, using a multigrid time-marching scheme. The initial unstructured mesh is successively refined based on gradients in the flow solution, with the multigrid levels being determined by the refinement procedure. Important issues related to solving viscous flows on unstructured meshes are discussed, These include calculation of the viscous stress terms in a manner that prevents wiggles, calculation of the time steps to include both inviscid and viscous effects, numerical smoothing considerations, minimization of computer storage requirements, and implementation of the k-epsilon turbulence model. Solutions are presented for several examples of industrial importance that illustrate the potential of the method, including transonic flow about an aircraft engine nacelle, and in both rotating and nonrotating turbomachinery passages.