Abstract

Natural heat convection of air and water and transient free convection with conduction and solidification of a ternary high temperature alloy inside square cavities are described by a three levels V cycle geometric multigrid and the finite volume method. The efficiency of the calculation procedure to characterize three-dimensional natural convection inside cubical cavities with and without liquid-solid phase change by the geometric multigrid is evaluated against the computation time required to solve each one of the three problems by a single staggered grid. The numerical simulations shows that the performance of the finite volume method increased when a geometric multigrid with a V cycle of three levels was used. Reductions in the computation time obtained by the multigrid scheme accounted to 35% for steady natural convection of air with a Rayleigh number Ra = 10(6) and of water with Ra = 2.2 x 10(5), and by a 15% for unsteady natural convection with heat diffusion in liquid to solid phase transformation at high temperature of an aluminum ternary alloy (Ra = 10(4)). The accuracy of the numerical results obtained for velocity and temperature distributions by the multigrid technique was verified with reliable numerical results reported for each problem.