An accuracy evaluation of unstructured node-centred finite volume methods

Authors:
Magnus Svärd;Jing Gong;Jan Nordström
Affiliations:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA and Centre of Mathematics for Applications, University of Oslo, P.B. 1053 Blindern, N-0316 Oslo, Nor ...;Department of Information Technology, Uppsala University, Uppsala, Sweden;Department of Information Technology, Uppsala University, Uppsala, Sweden and Department of Computational Physics, Division of Systems Technology, The Swedish Defense Research Agency, SE-164 90 St ...
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

Node-centred edge-based finite volume approximations are very common in computational fluid dynamics since they are assumed to run on structured, unstructured and even on mixed grids. We analyse the accuracy properties of both first and second derivative approximations and conclude that these schemes cannot be used on arbitrary grids as is often assumed. For the Euler equations first-order accuracy can be obtained if care is taken when constructing the grid. For the Navier-Stokes equations, the grid restrictions are so severe that these finite volume schemes have little advantage over structured finite difference schemes. Our theoretical results are verified through extensive computations.