A Parallel AMR Implementation of The Discrete Ordinates Method for Radiation Transport
Requirements for efficient parallel numerical computations fall into two broad categories: scalable algorithms and scalable implementations. For the discrete ordinates method the basic algorithmic building block is the transport sweep, and some form of convergence acceleration is required in order to combine sweeps into an efficient solver. This paper will focus on the implementation side of the issue. I will present a method for performing parallel transport sweeps in the context of a code for time-dependent radiation hydrodynamics using block-structured adaptive mesh refinement. Sweep patterns involving a single refinement level as well as sweeps coupling multiple levels will both be discussed. 2D and 3D numerical results will compare the parallel performance of these schemes with the multigrid solvers called by a radiation diffusion package implemented in the same code.
KeywordsCoarse Grid Adaptive Mesh Coarse Level Discrete Ordinate Discrete Ordinate Method
Unable to display preview. Download preview PDF.
- CL68.Carlson, B.G., Lathrop, K.D.: Transport theory—the method of discrete ordinates. In: Greenspan, H., Kelber, C.N., Okrent, D. (eds) Computing Methods in Reactor Physics. Gordon and Breach, New York (1968)Google Scholar
- CCF98.Chow, E., Cleary, A.J., Falgout, R.D.: Design of the hypre preconditioner library. Proceedings of the SIAM Workshop on Object Oriented Methods for Interoperable Scientific and Engineering Computing. Yorktown Heights, NY, October 21–23, 1998Google Scholar
- DS96.Dorr, M.R., Still, C.H.: Concurrent source iteration in the solution of three-dimensional, multigroup discrete ordinates neutron transport equations. Nucl. Sci. Eng., 122, 287–308 (1996)Google Scholar
- How02.Howell L.H.: A discrete ordinates algorithm for radiation transport using blockstructured adaptive mesh refinement. Proceedings of the Nuclear Explosives Code Development Conference. Monterey, CA, October 21–24, 2002Google Scholar
- HG98.Howell, L.H., Greenough, J.A.: A block-structured adaptive mesh refinement algorithm for diffusion radiation. Proceedings of the Nuclear Explosives Code Development Conference. Las Vegas, Nevada, October 25–30, 1998Google Scholar
- LM93.Lewis, E.E., Miller, W.F. Jr.: Computational Methods of Neutron Transport. American Nuclear Society, La Grange Park, IL (1993)Google Scholar
- Mat99.Mathews, K.A.: On the propagation of rays in discrete ordinates. Nucl. Sci. Eng., 132, 155–180 (1999)Google Scholar
- RAN97.Ramone, G.L., Adams, M.L., Nowak, P.F.: A transport synthetic acceleration method for transport iterations. Nucl. Sci. Eng., 125, 257–283 (1997)Google Scholar