Derivation and characteristics analysis of an acoustics-convection upstream resolution algorithm for the two-dimensional Euler and Navier-Stokes equations
The first of a two-paper series, this paper introduces a new decomposition not of the hyperbolic flux vector but of the flux vector Jacobian. The paper then details for the Euler and Navier-Stokes equations an intrinsically infinite directional upstream-bias formulation that rests on the mathematics and physics of multi-dimensional acoustics and convection. Based upon characteristic velocities, this formulation introduces the upstream bias directly at the differential equation level, before the spatial discretization, within a characteristics-bias governing system. Through a decomposition of the Euler flux divergence into multi-dimensional acoustics and convection-acoustics components, this characteristics-bias system induces consistent upstream bias along all directions of spatial wave propagation, with anisotropic variable-strength upstreaming that correlates with the spatial distribution of characteristic velocities. Copyright 2005 John Wiley & Sons, Ltd.
characteristics euler and navier-stokes equations cfd multi-dimensional upwind