Solving an inverse problem with four unknown boundary conditions in a lid-driven cavity with heated walls using the levenberg-marquardt method

This study investigates the application of the Levenberg-Marquardt method in solving inverse heat transfer problems for a lid-driven cavity with four unknown thermal boundary conditions. The direct problem is solved using computational fluid dynamics (CFD) techniques implemented in OpenFOAM, employing the URANS equations. The numerical framework is first validated against experimental data from literature for a cavity with known boundary conditions. The inverse analysis focuses on simultaneously estimating four wall temperatures using temperature measurements at various sensor locations. The effects of sensor quantity and placement, algorithm parameters (fractional increment and damping coefficient), and measurement noise on the solution accuracy are systematically examined. The algorithm demonstrates robust convergence using a fractional increment of 0.0001 and an initial damping value of 1.0. It also maintains stability and accuracy even when measurement noise reaches up to 10 % of the maximum temperature difference. Under various conditions, the proposed approach consistently converges in approximately 12 iterations, confirming its effectiveness for simultaneously estimating multiple thermal boundary conditions in enclosed cavities. This study contributes to the development of reliable inverse methods for industrial applications involving natural convection in temperature-controlled chambers.