Inverse estimation of unknown boundary geometry in a porous lid-driven cavity using Levenberg-Marquardt algorithm

Precise analysis of fluid flow and convective heat transfer is paramount for optimizing thermal engineering systems, yet direct access to internal geometric parameters is often restricted. This study develops a novel, automated inverse methodology to reconstruct the unknown wavy bottom geometry of an unsteady, porous lid-driven cavity undergoing mixed convection. The forward physical domain, incorporating Darcy-Brinkman-Forchheimer effects and mixed convection driven by an oscillating lid, is solved using OpenFOAM. To address the inherently ill-posed inverse problem, a Python-based Levenberg-Marquardt (L-M) optimization framework is dynamically coupled with the computational fluid dynamics (CFD) solver, enabling iterative geometric updates without manual remeshing interventions. The shape of the target boundary is parameterized via a flexible composite trigonometric function, and reconstruction relies on sparse discrete velocity measurements. Comprehensive sensitivity analyses systematically evaluate the impact of sensor placement, algorithm tuning parameters, and experimental noise. Results demonstrate that among the configurations tested, a two-sensor configuration positioned 0.6 m from the moving lid provides the best balance of information content and mathematical stability, minimizing the root-mean-square error to 1.17 × 10 − 2 m. Furthermore, tuning the algorithm parameters (μ = 0.1 and P d = 0.0001) ensures the most robust and stable optimization convergence. The framework effectively handles normally distributed measurement noise, preserving high geometric fidelity ( R 2 = 92.70 % ) up to noise levels of 25% of the maximum velocity, though physical reliability deteriorates significantly at 30%. Ultimately, the proposed approach demonstrates the feasibility of reconstructing complex boundaries and reproducing transient hydrodynamic fields under controlled numerical conditions.