A STAGGERED CONTROL-VOLUME SCHEME FOR UNSTRUCTURED TRIANGULAR GRIDS

The purpose of this work is to introduce and validate a new staggered control volume method for the simulation of 2D/axisymmetric incompress ible flows. The present study introduces a numerical procedure for sol ving the Navier-Stokes equations using the primitive variable formulat ion. The proposed method is an extension of the staggered grid methodo logy to unstructured triangular meshes for a control volume approach w hich features ease of handling of irregularly shaped domains. Two alte rnative elements are studied: transported scalars are stored either at the sides of an element or at its vertices, while the pressure is alw ays stored at the centre of an element. Two interpolation functions we re investigated for the integration of the momentum equations: a skewe d mass-weighted upwind function and a flow-oriented exponential shape function. The momentum equations are solved over the covolume of a sid e or of a vertex and the pressure-velocity coupling makes use of a loc alized linear reconstruction of the discontinuous pressure field surro unding an element in order to obtain the pressure gradient terms. The pressure equation is obtained through a discretization of the continui ty equation which uses the triangular element itself as the control vo lume. The method is applied to the simulation of the following test ca ses: backward-facing step flow, flow over a two-dimensional obstacle a nd flow in a pipe with sudden contraction of cross-sectional area. All numerical investigations are compared with experimental data from the literature. A grid convergence and error analysis study is also carri ed out for flow in a driven cavity. Results compared favourably with e xperimental data and so the new control volume scheme is deemed well s uited for the prediction of incompressible flows in complex geometries . (C) 1997 John Wiley & Sons, Ltd.