An anisotropic h-adaptive finite element method for compressible Navier-Stokes equations

Abstract

Application of the finite element method with significantly stretched elements to solve compressible Navier-Stokes equations is presented. Stretched elements are introduced in an adaptive process as a result of selective directional subsecting of elements. An adaptive strategy of such anisotropic h-type refinements was developed. It is based on minimization of the interpolation errors, reduction of the residual error indicators and an adaptive recovery of the viscous fluxes with the possibility to control their accuracy. An iterative solver with the convergence characteristics independent of the aspect ratio of elements is presented. The solver is the GMRES algorithm with the domain decomposition Schwarz-type preconditioner. The proposed techniques are used to solve a benchmark problem, a hypersonic high Reynolds number flow with strong shock-boundary layer interaction.