A method to form matrix equations with high-order schemes for convective term and an application to a complex geometry

This paper presents a method to solve equations with high-order schemes for convective term. The method was examined for a computational domain involving non-computational cells. First, a value for a cell face was given by QUICK and a second-order upwind method based on the finite volume method in the case of a non-uniform grid, and disretized equations were formulated. Second, the matrix equations were formed by using the discretized equations in the computational domain involving non-computational cells. This method was applied to a cavity flow and backward-facing step flow, and high accuracy was shown in both calculations. Furthermore, a duct flow with pillars in a staggered arrangement was also numerically analyzed. As a result, it was shown that this method is effective for complex geometries.