A hybrid finite element–finite volume method for incompressible flow through complex geometries using mixed grids

摘要

A simple, robust, local divergence free, second-order accurate, stable solution procedure for incompressible flows using a finite element method for the evaluation of velocity components and a finite volume method for the evaluation of pressure is presented. In order to ensure pressure stability, the velocity components (at vertices) and pressure (at cell centres) are evaluated at different points of the elements. The finite element–finite volume combinations are taken from triangular and quadrilateral grids. These grids are used alone or together as mixed grids. A new element-cell configuration consisting of two adjacent triangular elements together as a finite volume quadrilateral cell for the evaluation of pressure is introduced. Predictions are found to be in good agreement with the available results for all types of grids used. The present method combines the pressure stability of the staggered grid finite volume method (FVM) and the flexibility of the finite element approach to analyse flow through complex geometries; it is easy to implement and locally divergence free.