Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

This paper presents a new finite volume discretization methodology for the solution of transport equations on locally refined or unstructured Cartesian meshes. The implementation of the cell-face values of the dependent variables enables the employment of data from remote cells and thus the use of higher-order differencing schemes. It also results in simple and flux-conservative multiple-scale stencils for the discretization of the governing equations. The latter are finally cast into a generalized form that does not depend on the local mesh structure. The performance of the numerical model is demonstrated on some classical 2D problems using various gridding techniques and a bounded second-order upwind scheme. A stable and efficient behaviour of the algorithm is observed in all test cases. The results indicate that the combination in the present model of both local grid refinement and second-order discretization can produce substantially more accurate solutions than each of the above techniques alone, for the same computational effort. The method is also applicable to turbulent flows and can be easily extended to three-dimensions.