This paper introduces a novel platform that integrates three preconditioning matrices based on conservative variables: the Turkel, Choi-Merkle, and Onur matrices. The platform aims to compare these matrices in terms of accuracy and robustness by investigating their performance in solving three distinct and challenging high-gradient laminar flow problems: (i) Bi-plane NACA0012 airfoil, (ii) lid-driven flow in a square cavity, and (iii) flow in a planar T-junction. These problems serve as new and challenging test cases to accurately determine the abilities of the preconditioning matrices. The preconditioning matrices are applied to evaluate the numerical solutions, and their performance in complex flow fields is assessed in terms of accuracy and efficiency. By solving these flow problems, the effectiveness of the preconditioning matrices is thoroughly analyzed. By integrating these preconditioning matrices into a single platform, this paper significantly contributes to the field. The approach enables a direct and meaningful comparison of the performance of the Turkel, Choi-Merkle, and Onur matrices in solving these new and challenging laminar flow problems. Through a comprehensive evaluation, the strengths and weaknesses of each matrix are identified, highlighting their abilities to handle complex convective-oriented flow fields. The analysis of the three preconditioning approaches reveals a critical finding: although they provide identical accuracy results, they exhibit significant variations in terms of convergence acceleration rate. The condition number of the system of equations plays a crucial role in this aspect, as it directly affects the convergence rate of solutions, particularly in convective-oriented flow fields. Moreover, while viscosity is undoubtedly a critical factor in creating challenges for the performance of preconditioning matrices, it is also essential to consider the viscosity gradient rate governing the flow field. This gradient rate serves as a determining element in the effectiveness of the preconditioning matrix.

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