THE FINITE VOLUME PROJECTION METHOD WITH HYBRID UNSTRUCTURED TRIANGULAR COLLOCATED GRIDS FOR INCOMPRESSIBLE FLOWS

In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows.

Calculation of cell face velocity of non-staggered grid system

In this paper, the cell face velocities in the discretization of the continu- ity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations. Their performances are compared. When the linear interpolation is used to calculate the coefficients, the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution.

Six Convective Difference Schemes on Different Grid Systems for Fluid Flow and Heat Transfer with SIMPLE Algorithm

Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow and heat transfer based on the finite volume method using staggered and Rhie-Chow’s momentum interpolation collocated grids, the second part contains the comparative computations being conducted on Rhie-Chow’s momentum interpolation collocated grid and Thiart’s finite difference scheme based nonstaggered grid. Three 3-D cases that have analytical or benchmark solutions are adopted. For the first part, the results of computations indicate that, all the six schemes have the same numerical accuracy when the diffusion term is predominant. With the increase of convection, the FUDS, HDS and PLDS almost have the same accuracy in two of those grid systems, while the SUDS and QUICK have higher accuracy than the former. The accuracy of CDS is something in between. For the same under-relaxation factors and convergence criterion, the convergence rate of each scheme on those two grid systems are nearly equal with that on the staggered grid being a little bit faster. For QUICK and CDS, smooth, non-oscillating solutions can be obtained even when local Peclet number may be as large as 31.2-31.3. For the second part, it is concluded that simplified collocated grid system is preferable from numerical accuracy, grid Peclet number limit, sensitivity to the underrelaxation factor and the freedom in choosing finite difference scheme for convection term.