An unsteady incompressible numerical method for the solution of Navier-Stokes equations is presented. The finite volume solver adopts the method of artificial compressibility, using an implicit dual time stepping scheme for time accuracy. The 2D solver operates on general hybrid meshes containing triangles and quadrilaterals, while the 3D solver operates on hybrid meshes containing tetrahedra, pyramids, prisms and hexahedra. The developed algorithms for spatial discretization and time integration are mesh transparent. An upwind spatial discretization scheme is used for the convective terms and a central scheme for the diffusive terms. Efficient calculation of flow fluxes is implemented in an edge-wise fashion. A new combined method for efficient and accurate evaluation of variable gradients is achieved by using an averaging technique and by avoiding multiple spatial integration of the same element of the mesh. The results obtained agree well with numerical solutions obtained by other researchers.

Purpose -The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer. Design/methodology/approach -A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach. Findings -A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase. Practical implications -Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels. Originality/value -A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe's approximate Riemann solver is proposed.

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