A 3D second‐order accurate projection‐based Finite Volume code on non‐staggered, non‐uniform structured grids with continuity preserving properties: application to buoyancy‐driven flows

It is well known that exact projection methods (EPM) on non-staggered grids suffer for the presence of non-solenoidal spurious modes. Hence, a formulation for simulating time-dependent incompressible flows while allowing the discrete continuity equation to be satisfied up to machine-accuracy, by using a Finite Volume-based second-order accurate projection method on non-staggered and non-uniform 3D grids, is illustrated. The procedure exploits the Helmholtz–Hodge decomposition theorem for deriving an additional velocity field that enforces the discrete continuity without altering the vorticity field. This is accomplished by first solving an elliptic equation on a compact stencil that is by performing a standard approximate projection method (APM). In such a way, three sets of divergence-free normal-to-face velocities can be computed. Then, a second elliptic equation for a scalar field is derived by prescribing that its additional discrete gradient ensures the continuity constraint based on the adopted linear interpolation of the velocity. Characteristics of the double projection method (DPM) are illustrated in details and stability and accuracy of the method are addressed. The resulting numerical scheme is then applied to laminar buoyancy-driven flows and is proved to be stable and efficient. Copyright © 2006 John Wiley & Sons, Ltd.