Travis Trahan

Over the last half century, two distinct methods for modeling radiation transport have been developed: stochastic (Monte Carlo), based on simulating a large number of random particle histories; and deterministic, based on discretizing the transport equation in space, angle, and/or energy. Only recently has an attempt been made to merge the two methodologies together, utilizing the strengths and suppressing the weaknesses of each. Hybrid methods for radiation transport employ both deterministic and stochastic methods. For example, a simple deterministic method can be used to estimate the solution, and this information can be used to distribute particles more uniformly in a Monte Carlo simulation using well−established variance reduction techniques. Other deterministic techniques can be used to make more efficient use of, and to extract more information from, Monte Carlo simulations. In these ways, hybrid methods can efficiently create a smaller, more uniform variance, effectively decreasing the run time of a given simulation. Hybrid methods have been applied almost exclusively to linear problems of neutron transport for nuclear reactor applications. My research will focus on the development of hybrid methods for thermal radiation transport (TRT) -- the nonlinear, time−dependent process of high−energy photons penetrating a relatively cold plasma. TRT problems are extraordinarily difficult, yet are of great interest to the DOE in its stockpile stewardship program. Currently, simulating practical TRT problems without approximation is extremely costly, and is done only with codes that are either purely deterministic or purely stochastic. My research will develop new hybrid methods for TRT that will use both methodologies, suppressing the deficiencies of each.

T.J. Trahan, J.C. Ragusa, J.E. Morel, "GALERKIN-QUADRATURES FOR SOLVING FORWARD-PEAKED SCATTERING PARTICLE TRANSPORT PROBLEMS WITH THE SN METHOD IN 2D CARTESIAN GEOMETRIES," Proceedings of the International Conference on Mathematics, Computational Methods & Reactor Physics, Saratoga Springs, New York, May 3-7, 2009.

E.W. Larsen, T.J. Trahan, "2-D Anisotropic Diffusion in Optically Thin Channels", Transactions of the American Nuclear Society Vol. 101, pp. 387 (2009).