Anisotropic grid adaptation for Navier–Stokes’ equations

Navier–Stokes’ equations are discretized in space by a finite volume method. Error equations are derived which are approximately satisfied by the errors in the solution. The dependence of the solution errors on the discretization errors is analyzed in certain flow cases. The grid is adapted based on the estimated discretization errors. The refinement and coarsening of the grid are anisotropic in the sense that it is different in different directions in the computational domain. The adaptation algorithm is applied to laminar, viscous flow over a flat plate, in a channel with a bump, and around a cylinder and an airfoil.