A second-order-accuracy finite difference scheme for numerical computation on two-dimensional three-neighboring-node unstructured grids

The computation of the finite difference method in curvilinear coordinates usually necessitates coordinate transformation. Eliminating geometric errors induced by coordinate transformation can be achieved with geometric conservation law. However, no research has been conducted to implement a difference scheme on two-dimensional three-neighboring-node unstructured meshes and achieve a second-order accuracy. In this paper, a new finite difference method is proposed for a numerical simulation on these meshes, and it can achieve a second-order accuracy with the use of the gradient interpolation and the discrete criterion, freezing the metrics and Jacobian at local nodes. The results of several numerical tests demonstrate that the method achieved reliable performance and robustness on unique and randomized unstructured grids for a complex flow with discontinuity, subsonic inflow, and diffraction. The method had comparable accuracy to the second-order difference scheme on structured grids.