Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Abstract

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained

Comparative Study of UNIFAES and other Finite-Volume Schemes for the Discretization of Advective and Viscous Fluxes in Incompressible Navier-Stokes Equations, Using Various Mesh Structures

“…Again it presented very good performance, generally overcoming the other schemes, except central differencing in a range of Peclet numbers where this scheme showed extremely high accuracy and unusual stability up to Peclet number 10,000. It also presented very good performance in simple one-dimensional tests concerning grid irregularity [23,24].…”

“…where P AE was put by Llagostera [23,24] in a form fully adequate for using the power law or other approximation to the function p(p): …”

“…The power law approximation was also employed in the UNIFAES [22][23][24]. On the other hand, the greater time requirement of these schemes also made the meshes for Navier-Stokes equations with collocated velocity components more attractive, even in orthogonal regular geometries, for allowing the influence coefficients at each node to be calculated only once per iteration for all momentum components.…”

“…Finally, the power law form of the UNIFAES was submitted to the transport equation on buoyant Darcian porous flows involving natural and mixed convection in different geometries [22][23][24]. Some comparisons with the simple power law scheme also showed the crescent superiority of the UNIFAES as the Rayleigh number increased.…”

A semi‐staggered finite volume approach applied to two‐ and three‐dimensional flow in channels with gradual expansions

“…Well-known limitations of the simple exponential scheme 25,26 are not shared by more sophisticated schemes of this class. Among those, UNIFAES has been demonstrating excellent accuracy and stability, [27][28][29][30][31] with moderate increase of computational complexity compared to the simple exponential. The semi-staggered mesh, 32,33 also called half-staggered [34][35][36] or hybrid staggered, [37][38][39] uses vertex co-located velocity components and cell-centered pressure nodes.…”