Two-dimensional implicit time dependent calculations for incompressible flows on adaptive unstructured meshes

A flow solver originally developed for the solution of the two-dimensional unsteady inviscid incompressible equations on unstructured triangular meshes was extended to compute laminar viscous flows with a dynamic mesh adaptation method. The use of a mesh adaptation method allows one to obtain higher accuracy, lower computational cost, or both as compared with a suitably refined static mesh. Mesh derefinement is important for efficient numerical simulation of time dependent flows where the relevant features of the flow change with time. The use of unstructured triangular meshes allows the straightforward computation of complex configurations.; The numerical algorithm is based on a dual time stepping fully implicit multigrid-driven algorithm. Time dependent calculations are performed implicitly by regarding each time step as a steady-state problem in pseudotime. The method of artificial compressibility is used to solve the flow equations. The dynamic mesh adaptation method performs local mesh refinement using an incremental Delaunay algorithm and mesh coarsening by means of an edge collapse. A mesh coarsening algorithm generates the sequence of coarser grids for multigrid from the adapted fine mesh.; The method is verified by grid refinement studies and time resolution studies to demonstrate the order of the scheme. Numerical simulation of low Reynolds number flow over a shedding circular cylinder shows good agreement with experimental results and other computational results.