Solution of incompressible flows with or without a free surface using the finite volume method on unstructured triangular meshes
An incompressible Navier-Stokes solver based on a cell-centre finite volume formulation for unstructured triangular meshes is developed and tested. The solution methodology makes use of pseudocompressibility, whereby the convective terms are computed using a Godunov-type second-order upwind finite volume formulation. The evolution of the solution in time is obtained by subiterating the equations in pseudotime for each physical time step, with the pseudotime step set equal to infinity. For flows with a free surface the computational mesh is fitted to the free surface boundary at each time step, with the free surface elevation satisfying a kinematic boundary condition. A 'leakage coefficient', epsilon, is introduced for the calculation of flows with a free surface in order to control the leakage of flow through the free surface. This allows the assumption of stationarity of mesh points to be made during the course of pseudotime iteration. The solver is tested by comparing the output with a wide range of documented published results, both for flows with and without a free surface. The presented results show that the solver is robust. Copyright (C) 1999 John Wiley & Sons.
finite volume method unstructured triangular mesh navier-stokes solver leakage coefficient method of pseudocompressibility free surface flows