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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.
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Antoine Dumon, Cyrille Allery, Amine Ammar. Simulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD). Numerical Heat Transfer, Part B: Fundamentals An International Journal of Computation and Methodology, 2013, 63 (1), pp.18-43. ⟨10.1080/10407790.2012.724991⟩. ⟨hal-01207113⟩

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