Conservative preconditioning techniques for efficient compressible and incompressible flow simulations on unstructured meshes

Abstract Three preconditioning methods suggested by Eriksson, Choi, Merkel, and Turkel have been utilized within a 2D upwind Euler flow solver designed for unstructured grids. These strategies efficiently address the complexities of steady inviscid flows at low Mach numbers. The conservative formulations of the preconditioning matrices are rigorously derived. This implementation enables a more accurate evaluation of high‐gradient flows. Extensive simulations are conducted on various flow scenarios, including flows over the NACA0012 airfoil, a multi‐element three‐element airfoil, and a smooth bump with varying Mach numbers, to validate the effectiveness of the aforementioned preconditioning strategies. Compared to the non‐preconditioned approach, the results demonstrate significant accuracy and convergence speed improvements for all three preconditioning methods. These strategies exhibit remarkable efficiency for low Mach and incompressible flows. Among the three approaches, the Turkel preconditioner stands out with its optimal condition number, leading to superior performance. For low Mach numbers, convergence is accelerated by up to 88%, while at transonic speeds, it still achieves a notable 38% increase in convergence speed. Additionally, the preconditioning techniques preserve solution accuracy near challenging stagnation points. This study establishes a unified conservative framework for assessing preconditioning approaches and highlights their ability to resolve the complex fluid physics of low Mach number flows on unstructured grids. The findings underscore the significance of employing such strategies to enhance accuracy and computational efficiency in evaluating high‐gradient flows.