Parallel solutions of a 2-D phase change problem on a hypercube
Hira Narang, John B. Drake · 1989
This report documents the model, algorithms, and results for a heat transfer problem with phase change simulated numerically on a hypercube parallel computer. The temperature and enthalpy distribution in a rectangular domain with first kind boundary conditions (temperature prescribed) is found as a function of time. The model involves a non-linear partial differential equation with a constitutive relation between enthalpy and temperature. The solution to the system is obtained by finite difference approximation with both explicit and implicit methods. In the implicit case, a successive overrelaxation technique with red, black ordering is implemented. The efficiency of the explicit method is compared with that of the implicit method in a multiprocessor computing environment. The design, development, and implementation of algorithms targeted INTEL's iPSC/2 hypercube involving up to 64 processors. The computational workload was uniformly divided among processors as fast as possible by dividing the finite difference grid into several strips and assigning each strip to a processor. The results, depicted in terms of tables, show the effect of relaxation parameter, and stepsize on the efficiency of the parallel algorithms. This is contrasted with the sequential algorithms. 16 refs., 6 figs., 15 tabs.