Keywords: finite volumes, incompressible flow, internal flow.

The scope of this paper is to compare the continuity vorticity pressure (CVP), the auxiliary potential and implicit potential (IPOT) methodologies for the solution of laminar incompressible developing flow with buoyancy forces in a straight square duct. The CVP variational equations method was pioneered by Hatzikonstantinou et al. [1]. Its formulation is based on a well known vector identity which facilitates the computation of the velocity corrections based on the continuity residual. The auxiliary potential method [2] bares many similarities to the simplified marker and cell (SMAC) scheme, as it involves a potential velocity through which the velocity and pressure corrections are determined. However, it is not based on a time-step technique as the SMAC scheme and it can be easily applied to steady state problems. The IPOT method is a recently created method which is characterized by great simplicity. Its main property is that it does not involve the solution of any partial differential equations apart from the ones for the momentum. The pressure correction that is required in its formulation is directly linked to the continuity residual.

The scope of this paper is to present a critical comparison of the three methodologies, applied to laminar incompressible developing flow with buoyancy forces in a straight square duct. The comparison concerns the convergence properties, the robustness, the accuracy and the functionality of each methodology and highlights the advantages and disadvantages of each approach. The results show that although all three methods can predict accurately the development of the flow for low Reynolds numbers, they have their unique properties: the CVP method is the most demanding in terms of the equations that must be solved, but it is also characterized by increased robustness and computational efficiency; the auxiliary potential method has great functionality but it can be slower than CVP; the IPOT method is the simplest, fastest and most flexible of the three but its lacks robustness and requires the use of a relaxation parameter.

1

P.M. Hatzikonstantinou, V.D. Sakalis, "A numerical-variational procedure for laminar flow in curved square ducts", Int. J Numer. Methods Fluids, 45, 1269-1289, 2004. doi:10.1002/fld.596

2

P.K. Papadopoulos, "An auxiliary potential velocity method for incompressible viscous flow", Computers and Fluids, 2011. doi:10.1016/j.compfluid.2011.07.016

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