An efficient cell-centered finite-volume method with face-averaged nodal-gradients for triangular grids

Abstract

In this paper, a face-averaged nodal-gradient approach is proposed as an efficient gradient method for a second-order cell-centered finite-volume discretization on triangular grids. The gradients needed in the linear reconstruction are computed in two steps: (1) compute gradients at nodes from solutions stored at cells, and (2) compute the gradient at each face by averaging the nodal gradients over the nodes forming the face. A unique feature of the proposed approach is that the same face-averaged gradient is used in linear reconstructions from both the left and right cells to the face centroid. This approach offers advantages over a conventional cell-gradient-based finite-volume method: reduced memory requirement for the gradients, smaller residual stencils, direct evaluations of viscous stresses and heat fluxes at solid boundaries, and less interpartition communication. The method is demonstrated for various inviscid and viscous problems from low to high Mach numbers on triangular grids.