Spatial discretization algorithm for cell-centered finite volume method based on face gradient reconstruction

The gradient reconstruction process determines the spatial discretization accuracy and robustness of the finite volume method. A novel gradient reconstruction method is proposed for the cell-centered finite volume method. Based on the weighted least squares principle, this method calculates the face-centered variables and the gradient of these variables and then solves the cell-centered gradient using either central difference or arithmetic averaging methods for different grid types. Finally, a new boundary constraint algorithm adapted to the new gradient reconstruction method is developed by combining boundary conditions with the gradient reconstruction process. A grid convergence study using an exact test function shows that the new method can achieve the linear reconstruction of the full-field gradient under smooth solution conditions. A series of inviscid and viscous flow cases show that, compared with the previous method, this method can effectively reduce the numerical dissipation in the near boundary region and improve the computational accuracy with better robustness under the large aspect ratio triangular grid.