Assessment of the finite volume method applied to the v2 − f model

Abstract

AbstractThe objective of this paper is to assess the accuracy of low‐order finite volume (FV) methods applied to the v2 − f turbulence model of Durbin (Theoret. Comput. Fluid Dyn. 1991; 3:1–13) in the near vicinity of solid walls. We are not (like many others) concerned with the stability of solvers ‐ the topic at hand is simply whether the mathematical properties of the v2 − f model can be captured by the given, widespread, numerical method. The v2 − f model is integrated all the way up to solid walls, where steep gradients in turbulence parameters are observed. The full resolution of wall gradients imposes quite high demands on the numerical schemes and it is not evident that common (second order) FV codes can fully cope with such demands. The v2 − f model is studied in a statistically one‐dimensional, fully developed channel flow where we compare FV schemes with a highly accurate spectral element reference implementation. For the FV method a higher‐order face interpolation scheme, using Lagrange interpolation polynomials up to arbitrary order, is described. It is concluded that a regular second‐order FV scheme cannot give an accurate representation of all model parameters, independent of mesh density. To match the spectral element solution an extended source treatment (we use three‐point Gauss–Lobatto quadrature), as well as a higher‐order discretization of diffusion is required. Furthermore, it is found that the location of the first internal node need to be well within y+=1. Copyright © 2009 John Wiley & Sons, Ltd.