Mathematical derivation of a finite volume formulation for laminar flow in complex geometries
Abstract
The mathematical derivation of a finite volume formulation of the NavierStokes equation is treated for general nonorthogonal curvilinear coordinates. The covariant velocity components are solved using this formulation, which leads to the pressurevelocity coupling becoming relatively easy to handle at the expense of a more complicated expression of the convective and diffusive fluxes. It is shown that, when using upwind differencing, the use of projected velocities gives better results than when curvature effects are included in the source term. The discretized equations are written in a form which enables the use of the tridiagonal matrix algorithm. The equations can be solved using either the SIMPLEC or PISO procedures. Two examples of laminar flows are given: (1) uniform flow using a cylindrical mesh, and (2) the flow inside a channel with a smooth expansion.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 May 1989
 DOI:
 10.1002/fld.1650090504
 Bibcode:
 1989IJNMF...9..531D
 Keywords:

 Finite Volume Method;
 Flow Geometry;
 Laminar Flow;
 NavierStokes Equation;
 Computational Fluid Dynamics;
 Computational Grids;
 Grid Generation (Mathematics);
 Matrices (Mathematics);
 Velocity Distribution;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer