A parallel adaptive numerical scheme for hyperbolic systems for conservation laws

We generalize the first author’s adaptive numerical scheme for scalar first order conservation laws to systems of equations in one space dimension. The resulting numerical method generates highly nonuniform, time-dependent grids, and hence is difficult to execute efficiently on vector computers such as the Cray or Cyber 205. In contrast, we show that this type of algorithm may be executed in parallel on alternate computer architectures. We describe a parallel implementation of the algorithm on the Denelcor HEP, a multiple-instruction, multiple-data (MIMD) shared memory parallel computer. This program dynamically partitions the problem domain so as to achieve effective load balancing among the available processes.