TWO-DIMENSIONAL TRANSFER EQUATION APPROXIMATION ON QUADRANGULAR AND POLYGONAL SPACIAL GRIDS WITH EXTENDED PATTERN DIFFERENCE SCHEME

N. P. Pleteneva, R. M. Shagaliyev
VANT. Ser.: Mat. Mod. Fiz. Rroc 1989. Вып.3. С. 34-41.

      For a two-dimensional transfer equation on quadrangular special grids a conservative finite-difference scheme with additional relations is derived in which grid values of the desired function are evaluated simultaneously, at vertexes (nodes), edges and centers of quadrangular grid cells. The difference transfer operator is of triangular structure. Results of numerical study are supplied showing second-order accurate convergence of the grid solution to the accurate one both on rectangular and on sufficiently non-orthogonal space grids. The scheme is extended to transfer equation numerical solution on grids of arbitrary convex polygonals.