A novel stencil selection method for the gradient reconstruction on unstructured grid based on OpenFOAM

Abstract

For the unstructured finite volume algorithms, the stencil utilized for gradient reconstruction is important for the accuracy, efficiency and robustness. In this paper, we present a novel stencil selection method for the gradient reconstruction of the cell-centered finite volume methodology. In the novel stencil selection method, two local directions are generated for each control volume, and the stencil is generated based on the local directions. In this way, the characteristics of the structured grid are able to be reflected on the unstructured grid. To obtain the suitable local directions, an advancing front technique (AFT) is utilized to guide their generation. Through AFT, the direction of the boundary normal vector, along which the flow fields change dramatically, is obtained and propagated from the boundaries to the internal regions. Finally, the novel stencil extends in two directions, one of which is approximately aligned with the direction of the boundary normal vector. Hence, the gradient reconstruction methods with the new stencil are able to use the information along the boundary normal. In order to verify the validity of the new stencil, we present a new gradient reconstruction method, the structured least squares (struLSQR) method, by applying the new stencil to the least squares (LSQR) method. The performance of struLSQR, and two existing gradient reconstruction methods in OpenFOAM is tested by adopting the 2D channel flow and the 2D circular cylinder flow on both the quadrilateral and the triangular grids. A laminar flow past a flat plate is also adopted to verify the applicability of struLSQR to the viscous flow. The numerical results illustrate that the new stencil is able to solve the blow-up problem of LSQR. It can also obtain a higher order of accuracy compared to extLSQR. Moreover, the convergence speed of struLSQR can be up to 1.64 ∼ 2.60x of that of extLSQR.