A vertex-weighted-Least-Squares gradient reconstruction

2017/02/15 by Fan Zhang, Zhang, Fan
Engineering · #76M12 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1702.04518

openalex publication_date 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient reconstruction method for cell-centered finite volume scheme is introduced. This method is composed of two successive steps. First, a vertex-based weighted-least-squares procedure is implemented to calculate vertex gradients, and then the cell-centered gradients are calculated by an arithmetic averaging procedure. By using these two procedures, extended stencils are implemented in the calculations, and the accuracy of gradient reconstruction is improved by the weighting procedure. In the given test cases, the proposed method is showing improvement on both the accuracy and convergence. Furthermore, the method could be extended to the calculation of viscous fluxes.

Related

• A generalized formulation for gradient schemes in unstructured finite volume method
• A family of first-order accurate gradient schemes for finite volume\n methods
• Implicit gradients based novel finite volume scheme for compressible single and multi-component flows
• A unification of least-squares and Green-Gauss gradients under a common projection-based gradient reconstruction framework
• Finite volume methods for incompressible flow