Theme 1-2-An efficient solution algorithm for dendritic channel networks using FEM or FDM

Abstract

This paper presents an efficient algorithm for solving one-dimensional flow equations through a dendritic channel network system. The equations generated through the finite element or the finite difference formulations can easily solved by applying the proposed algorithm without the requirement of substantial computer memory, even for a large network. An algorithm proposed earlier for linear finite elements has been extended here to cover its applicability towards using higher order finite elements and implicit finite difference schemes. The maximum active memory required in either case is only 2N x 2N where N is the number of branches of the network. The main advantage, perhaps, lies in the fact that the computational nodes of the branches can be numbered independently for each branch. The algorithm is suitable for programming on computers using parallel processing technology.