A third-order finite-volume residual-based scheme on unstructured grids

Abstract

A residual-based compact (RBC) scheme originally designed on structured grids has been extended to unstructured grids. A second and third-order finite-volume (FV) formulations of the residual-based scheme have been proposed, which rely on a linear or quadratic least-square based solution reconstruction and an original dissipation flux. A simple matrix-free implicit scheme provides robustness and fast-convergence to a steady-state. The schemes are extended from a steady inviscid formulation to viscous and unsteady flows, keeping the same design principles and successively including new contributions to the residual. Computations of 2D and 3D external flows proposed in the ADIGMA project are presented and analyzed. © 2010 Springer-Verlag Berlin Heidelberg.