ENTROPY CORRECTING SCHEMES AND NON-HIERARCHICAL AUTO-ADAPTIVE DYNAMICFINITE ELEMENT-TYPE MESHES - APPLICATIONS TO UNSTEADY AERODYNAMICS

This paper discusses the different sources of non-physical entropy pro duction which occur in the numerical resolution of the Euler equations for compressible inviscid flow and proposes several ways of correctin g these effects. In particular a hybrid corrected centred, augmented b y an accurate upwind scheme near singular boundaries is proposed which satisfies the mathematical entropy condition, and which solves the fl ow accurately within regions near non-smooth boundaries of the computa tional domain. A coupled new dynamic auto-adaptive mesh algorithm whic h produces highly accurate solutions is also introduced. This algorith m is non-hierarchical, i.e. it does not depend on a fixed background m esh, which allows structural and geometrical changes and generates ext remely precise discretizations for steady and unsteady flow.