Augmented weighted diamond form of the linear nodal scheme for Cartesian coordinate systems

The equations of the high order linear nodal numerical scheme are cast in an augmented weighted difference form for three dimensional cartesian nodes. The coupling exhibited by these equations indicate that this new algorithm is simpler and hence faster than previous nodal schemes of this degree of accuracy. A well-logging problem and a fast reactor problem are examined. The new scheme developed here is compared with the classical linear-linear nodal scheme and the diamond difference scheme. For the well-logging problem, it is found that the new scheme is both faster and simpler than the classical linear-linear nodal scheme while sacrificing little in accuracy. Even though the new scheme is more accurate than the diamond difference scheme for the reactor problem, the results indicate that state of the art acceleration methods are needed for nodal schemes