Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method

Abstract

A computational procedure is presented with an accelerated full-multigrid scheme for an efficient modeling of time-dependent buoyancy-driven flows. The smoother is the iterative red-and-black successive overrelaxation (RBSOR) scheme. In order to improve the convergence, an acceleration parameter, C, is implemented in the classical full-multigrid procedure. It is shown that an optimal value of C ¼ 3.75 minimizes the number of iterations needed for convergence. Numerical results are presented and compared with available investigations for an 8:1 differentially heated enclosure and a square heated cavity. Solutions for Prandtl number Pr ¼ 0.71, Rayleigh number Ra ¼ 3.4 3 10 5 for the 8:1 heated enclosure, and 10 5 e Ra e 10 9 for the square cavity are presented and show excellent agreement.

Obstacle Geometry Effect on the Stability of Two-Dimensional Incompressible Flow in a Channel

“…This method is used to discretize the equations and the projection method (Brown et al 2001) is also implemented to couple the momentum and continuity equations. Solving these equations was performed using an iterative method RBSOR (Red-Black Successive Over Relaxation) (Ben Cheikh et al 2007). The Poisson pressure correction equation is solved using a full multigrid method as suggested by Ben-Cheikh et al (2008).…”

Effect of Inclination on Heat Transfer and Fluid Flow in a Finned Enclosure Filled with a Dielectric Liquid

“…The advective terms are discretized using a QUICK third-order scheme proposed by Leonard [19] in the momentum equation and a second order central differencing one in the energy equation. The discretized momentum and energy equations are resolved using the red and black successive over relaxation method RBSOR [20], while the Poisson pressure correction equation is solved using a full multi-grid method as suggested by Ben Cheikh et al [21].…”

Three-dimensional Analysis of Mixed Convection in a Differentially Heated Lid-driven Cubic Enclosure

“…The discretized momentum and energy equations are solved employing the red and black successive over relaxation method (RBSOR) in Press et al [20], while the Poisson pressure correction equation is solved utilizing a full multi-grid method (Hortmann et al [21], Mesquita and de Lemos [22], Nobile [23]). If specific details about the computational methodology are needed, the reader is directed to Ben Cheikh et al [24]. Finally, the convergence of the numerical 3D velocity field and the 3D temperature .…”