Three-dimensional natural heat convection and ternary alloy solidification problems by finite volume geometric multigrid method

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 = 106 and of water with Ra = 2.2 × 105, 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 = 104). 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.