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.International audienceThe 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

Optimal flow control using a POD-based reduced-order model

“…Section 3 and Section 4 present the reduced optimization problem considering one and two control parameter(s), respectively. In Section 5, the different reduced models are applied to the control of the temperature in a heated lid-driven cavity, widely studied case in the literature [44][45][46]. Finally, the Section 6 concludes this paper while providing a discussion of the results.…”

Non-Intrusive In-Plane-Out-of-Plane Separated Representation in 3D Parametric Elastodynamics

“…In-plane-out-of-plane separated representations have been applied to solve elastic problems defined in plate [3], shell [4], extruded domains [5], multilayered composite structures [6,7], and were extended to cover many other physics: the solution of thermal problems [8]; the solution of the Navier-Stokes equations [9] and the simulation of heat and mass transfer [10]; the squeeze flows of Newtonian and non-Newtonian fluids in laminates in [11], among may others.…”

Non-intrusive proper generalized decomposition involving space and parameters: application to the mechanical modeling of 3D woven fabrics

“…The in-plane-out-of-plane decomposition was then extended to many other physics: thermal models were considered in [18]; squeeze flows of Newtonian and non Newtonian fluids in laminates in [21]; flows in stratified porous media in [22] an nonlinear viscoplastic flows in plate domains in [23]. A full space decomposition was also efficiently applied for solving the Navier-Stokes equations in the lid-driven cavity problem in [24][25][26].…”