An adaptive gradient correction method based on mesh skewness for finite volume fluid dynamics simulations

Abstract

In unstructured mesh solvers based on the finite volume method, accurate gradient calculation is crucial for determining the accuracy of equations. However, most mainstream computational fluid dynamics (CFD) software offer only uncorrected or globally corrected gradient options, which do not take into account local geometric characteristics. This limitation hampers computational efficiency and accuracy, especially in complex geometries, leading to poor convergence or even divergence, thus constraining its practical application in real-world engineering problems. To address these issues, this paper presents an adaptive gradient correction algorithm based on mesh skewness. By analyzing the geometric characteristics of mesh cells and dynamically applying a correction value, the algorithm modifies the gradient calculation formula adaptively to reduce numerical errors and improve accuracy, while ensuring stability. The algorithm has been successfully implemented in a general-purpose CFD software and validated through complex engineering cases such as sub-channel analysis, demonstrating its practical engineering value. Results indicate that for turbulent flow through a pipe, the proposed adaptive correction algorithm achieves an improved accuracy, demonstrating high precision and superiority in capturing intricate details of turbulence. In more complex scenarios like sub-channel analysis, the adaptive correction algorithm yields an error of 2.54% compared to 4.03% for the uncorrected approach. Unlike global correction methods that may lead to computational divergence within a few iterations, the adaptive correction method consistently maintains stability, accelerates convergence, and improves accuracy, offering significant theoretical and practical value.