Riemann solvers for time -dependent transport based on the maximum entropy and spherical harmonics closures.

A Roe-type Riemann solver is used to solve the spherical harmonics and maximum entropy approximations to the time-dependent neutron transport equation. The maximum entropy closure for the two-moment approximation of the transport equation is presented. It is based on the use of the most likely form of the distribution, restricted by certain constraints, to close the equations. It is designed to have a wider range of applicability than a linear two-moment closure. The spherical harmonics expansion of the transport equation is also reviewed. The high-resolution interpolation scheme of standard Riemann solvers has been modified to work with these closures. Three boundary conditions for use with the Riemann solver and the two closures have been developed and are described. They essentially provide the Mark and Marshak boundary conditions, and an extension of the Marshak boundary conditions. The maximum entropy closure does well in deep penetration problems but has difficulties if there is more than one special direction in the problem. For a pulsed isotropic line source the spherical harmonics produce a negative scalar flux at very early times. For less severe problems, or after a few collision times, even low-order spherical harmonics approximations yield excellent results. The Riemann solver provides an exceptionally robust method for numerically solving the resulting equations.Ph.D.Applied SciencesNuclear engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132743/2/9990853.pd