Modified algorithms for nonconforming taylor discretization

Abstract

Algorithms for solving partial differential equations which extend previous applications of the nonconforming Taylor discretization method (NTDM) are presented. In one modification the number of interrelated grid points is variable, thus enabling additional geometric flexibility. Another modification is the approximation of the governing differential equation using the method of weighted residuals. A simple one-dimensional test case with a known analytic solution is solved using this code. The results demonstrate that precision is enhanced when using the method of weighted residuals with an increased number of interrelated points. The algorithm is applied as a general purpose two-dimensional code for nonlinear steady state heat-conduction. Two-dimensional examples with complex geometry and boundary conditions are then solved both by the NTDM and by the finite elements method (FEM). The results obtained by the two methods are compared.