Reliable Finite Volume Methods for Navier Stokes Equations

The use of adaptive mesh spatial discretisation methods, coupled spatial and temporal error control and domain decomposition methods make it possible to construct efficient automatic methods for the numerical solution of time-dependent Navier Stokes problems. This paper describes the unstructured triangular mesh spatial discretisation method being used in a prototype package for compressible flows. The scheme is a cell-centred, second-order finite volume scheme that uses a ten triangle stencil. Previous work has concentrated on algorithms and error estimates for convection dominated problems. In this paper the algorithm is extended to include a new treatment of the diffusion terms. The prototype software uses an adaptive time error control and space remeshing strategy is used to attempt to control the numerical error in the solution.