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A scheme for the numerical simulation of incompressible flows is presented. The modeling equations are written in conservation law form. The algorithm, written in a delta form, is very robust without resorting to any degree of relaxation. The well-known cumbersome numerical implementation related to staggered grids is totally removed. The scheme is second-order-accurate in space and first-order in time. An important novelty is the separation of the pressure terms in the physical equations in a pressure flux, facilitating the tackling of different fluids. The algorithm has been applied to laminar and turbulent flows. The results are truly encouraging.

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Fluid flows along a shallow cavity. A numerical study was conducted to investigate the effects of heating the floor of the cavity. In order to draw a broader perspective, a parametric analysis was carried out, and the influences of the following parameters were investigated: (i) cavity aspect ratio, (ii) turbulence level of the oncoming flow, and (iii) Reynolds number. A finite-difference computer code was used to integrate the incompressible Reynolds-averaged Navier–Stokes equations. The code, recently developed by the authors, is of the pressure-based type, the grid is collocated, and artificial smoothing terms are added to control eventual odd–even decoupling and nonlinear instabilities. The parametric study revealed and helped to clarify many important physical aspects. Among them, the so called “vortexes encapsulation,” a desirable effect, because the capsule works well as a kind of fluidic thermal insulator. Another important point is related to the role played by the turbulent diffusion in the heat transfer mechanism.

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