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

摘要

This paper discusses the different sources of non-physical entropy production which occur in the numerical resolution of the Euler equations for compressible inviscid flow and proposes several ways of correcting these effects. In particular a hybrid corrected centred, augmented by an accurate upwind scheme near singular boundaries is proposed which satisfies the mathematical entropy condition, and which solves the flow accurately within regions near non-smooth boundaries of the computational domain. A coupled new dynamic auto-adaptive mesh algorithm which produces highly accurate solutions is also introduced. This algorithm is non-hierarchical, i.e. it does not depend on a fixed background mesh, which allows structural and geometrical changes and generates extremely precise discretizations for steady and unsteady flow.