An Exponentially Fitted Finite Volume Method for the Numerical Solution of 2D Unsteady Incompressible Flow Problems

Abstract

In this paper we develop and test an exponentially fitted finite volume method for the numerical solution of the Navier-Stokes equations describing 2D incompressible flows. The method is based on an unstructured Delaunay mesh and its dual Dirichlet tessellation, combined with a locally constant approximation to the flux. This yields a piecewise exponential approximation to the exact solution. Numerical tests are presented for a linear advection-diffusion problem with boundary layers. The method is then applied to the driven cavity problem with Reynolds numbers up to 10 4. The numerical results indicate that the method is robust for a wide range of values of the Reynolds number. In the case Re = 10 4 unsteady solutions are captured if the mesh is sufficiently fine.