For first order schemes, these disturbances may be understood in the context of viscous shock profiles and the relevant theories. The results also bear on higher order shock-capturing schemes, since they all reduce to first order near shock fronts in order to maintain monotonicity. The phenomenon will be discussed and results will shown. The method of discrete ordinates is commonly used to solve the Boltzmann transport equation. Numerically, these techniques raise issues for gridding and discretization strategies, iterative vs direct solvers, and methods for accelerating convergence.
Parallel computation poses additional challenges because of directional and long-range effects.
In this talk I'll highlight some of the interesting questions that arise in discrete ordinates transport from a numerical and computer science perspective. I'll discuss in some detail a new method we're pursuing at Sandia, to develop parallel direct solvers for radiation on unstructured grids, including some unsolved problems we have. And I'll show some performance results for how these computations scale on the large ASCI machines at the DOE labs and what implications this has for future trends in supercomputer architectures. These systems are environmentally sensitive and economically important. Consequently there has been a significant effort in the numerical approximation of these problems for a number of years.