Stability Analysis of Preconditioned Approximations of the Euler Equations on Unstructured Meshes

Abstract

This paper analyses the stability of a discretisation of the Euler equations on 3D unstructured grids using an edge-based data structure, first-order characteristic smoothing, a block-Jacobi preconditioner and Runge-Kutta time-marching. This is motivated by multigrid Navier-Stokes calculations in which this inviscid discretisation is the dominant component on coarse grids. The analysis uses algebraic..