Research

CCS-4 is also doing basic numerical transport methods research in support of the ASC Program.

One effort is the development of residual Monte Carlo methods for discrete systems. Results indicate that the residual Monte Carlo method is several orders of magnitude faster than the conventional Monte Carlo method for discrete nonlinear radiative diffusion calculations with standard cell-centered differencing. This suggests the possibility of constructing extremely efficient preconditioners for discrete radiative diffusion calculations in multidimensions using residual Monte Carlo techniques.

Another area of research is the development of a hybrid Implicit Monte Carlo (IMC)/diffusion technique for radiative transfer calculations. We have completed the development of a hybrid multigroup IMC/diffusion scheme that should be both accurate and highly efficient.

In deterministic transport, we are studying discontinuous finite-element (DFEM) discretizations for the one-dimension and two-dimension radiation-hydrodynamics equations with fully iterated nonlinear solution techniques. Investigations of the one-dimensional DFEM radiation-hydrodynamics equations has shown that flux-limiting can be a serious impediment to achieving fully iterated nonlinear solutions using the Newton-Krylov method. This difficulty was not anticipated and may require us to change our overall approach.

Lastly, CCS-4 personnel are looking at Krylov solution techniques for the three-dimensional unstructured-mesh SN equations with partially-consistent DSA preconditioning. By using DSA as a preconditioner in conjunction with a Krylov method, we have been able to obtain a solution technique for 3-D unstructured-mesh SN calculations that seems to be unconditionally effective. This is in contrast to the standard DSA method, which becomes ineffective in multidimensional problems with severe cross-section discontinuities.