Numerical Analysis Group Research Report NA-91/12

P I Crumpton, J A Mackenzie, K W Morton

Finite volume methods on a structured quadrilateral or hexahedral mesh have very attractive properties for the first order Euler equations, with the cell vertex scheme being preferred for its accuracy and greater compactness.

Somewhat surprisingly, though this scheme is less compact than its competitors for the second order convection-diffusion or Navier-Stokes equations, its accuracy properties are even more remarkable, being attained with no upwinding parameters. However, there are difficulties in setting up and solving an appropriate set of cell residual equations. In this paper we present a consistent cell vertex discretisation, together with multigrid pseudo-time stepping procedures which come close to setting the cell residuals to zero; the generalised Lax-Wendroff procedure that is used is a significant difference from previous attempts to use similar schemes.

Results are given for laminar flow, where careful comparisons are made to demonstrate accuracy, and turbulent flow with an algebraic turbulence model.

Subject classifications:

AMS(MOS): 76-08 65N99

Key words and phrases:

cell vertex, finite volume, Lax-Wendroff, compressible Navier-Stokes