Parallel Approach to the Nodal Method Solution of the Two-Dimensional Diffusion Equation.

摘要

The neutron diffusion equation in two-dimensional geometry is solved using the nodal method formalism. Three systems of equations arise in the solution: the x-current continuity equations, the y-current continuity equations and the balance of neutrons equations. An iterative procedure is developed to solve for the surface fluxes and cell-averaged fluxes by de-coupling the set of balance equations from the two current continuity systems. The iteration is initiated in the balance equation which supplies the starting estimates of the cell-averaged fluxes. These estimates are fed into the uncoupled, tridiagonal sets of x-current and y-current equations which can be solved independently of each other, so that the surface fluxes can be computed. The resulting surface fluxes are substituted into the balance equations to update the cell-averaged fluxes. These updated values become the new iterates. The independent nature of the x- and y-current continuity equations becomes the focal point of parallelism. The algorithm is implemented on two types of parallel machines -- the INTEL iPSC/2 hypercube which belongs to the class of distributed memory processors and the Sequent balance 8000 which is a shared memory computer. Results indicate the algorithm to be better suited for a shared memory environment. 10 refs., 1 fig., 2 tabs.