Simulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD)

Abstract

The aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model approach which consists of solving a partial differential equation while seeking the solution in separated form. Comparisons with results in the literature and with results from a standard solver are make. For the case of a mixed-convection problem without mass transfer, three Richardson numbers are considered, Ri = 0.1, Ri = 1, and Ri = 10. In this case, PGD is seven times faster than the standard solver with Ri = 10 with a similar accuracy. For the case with mass transfer, simulations are done with different Lewis numbers, Le = 5, Le = 25, and Le = 50, and with different value of the ratio N between the solutal and the thermal Grashoff numbers. In this case, too, PGD is ten times faster than the standard solver.