Title: A vertex-weighted-Least-Squares gradient reconstruction,
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.