Adaptive methods for compressible Euler and Navier-Stokes equations

The subject matter of the paper is the numerical solution of multidimensional hyperbolic conservation laws for compressible fluid flow. The basic system consists of the continuity equation, Euler or Navier-Stokes equations and energy equation. The inviscid system is discretized by the finite volume method based on upwind Aux vector splitting schemes. Special attention is paid to a suitable adaptive mesh refinement strategy for a precise identification and resolution of shock waves. The main purpose of this paper is the numerical comparison of the proposed shock indicator with a residual based error indicator. The operator splitting is used for the solution of viscous system. The viscous terms are discretized by the finite element method and a combined finite volume - finite element scheme is developed for the numerical solution of the complete viscous system. Some results of numerical simulation of gas flow arising from the industrial applications are presented. The comparison of numerical results with experimental data is discussed.