A Two-Dimensional Complete Flux Scheme in Local Flow Adapted Coordinates

Abstract

We present a formulation of the two-dimensional complete flux (CF) scheme in terms of local orthogonal coordinates adapted to the flow, i.e., one coordinate axis is aligned with the local velocity field and the other one is perpendicular to it. This approach gives rise to an advection-diffusion-reaction boundary value problem (BVP) for the flux component in the local flow direction. For the other (diffusive) flux component we use central differences. We will demonstrate the performance of the scheme for several examples.

Compact High Order Complete Flux Schemes

“…This way we have to compute an advection-diffusion flux component aligned with the flow, for which we can use the high order scheme, and a diffusion flux component perpendicular to the flow, for which we can use a compact scheme. In [5] we have carried out this procedure for the standard complete flux scheme. Finally, extension to time-dependent problems is probably the most troublesome.…”