Perturbational finite volume method for the solution of 2-D Navier-Stokes equations on unstructured colocated meshes

摘要

In this paper, perturbational finite volume (PFV) method of the Navier-Stokes equations for incompressible flow is developed. PFV scheme retains the advantages of second-order accurate central finite volume (2CFV) scheme. Both of them have the same terse formulation and use the same nodes. However, the interpolation approximation of PFV scheme is of higher order accurate. In PFV method, higher order accurate of the interpolation approximation is obtained by a numerical value pertubation technique, i.e. the mass fluxes of the cell faces are expanded into power series of the grid spacing and the coefficients of the power series are determined with the aid of the conservation equation itself. PFV schemes are used to compute the flow in a lid-driven cavity. The SIMPLE algorithm is used to predict the pressure-velocity coupling correction. Numerical results show that PFV scheme has higher accuracy, higher resolution, better stability and wider applicable range of Reynolds number than those of 2CFV scheme. For instance, in the case of coarse grid, the applicable Reynolds number ranges of second and fourth orders accurate PFV schemes are about a thousand times greater than that of 2CFV scheme.