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Center for Nonlinear Studies |
To solve the neutron transport equation, we use the P_N equations, which involve the approximate $(N+1)th$ moment to derive the closed $P_N$ equations. The $(N+1)th$ moment is obtained from the first known $N$ moments which are taken with respect to the Legendre polynomials. Entropy based closures get this approximation by minimizing the entropy functional under the first $N$ moment equation constraints.
Since we need to get the approximation at each discretized point and at every time, in practice, there is a need to efficiently solve the minimizing entropy problem. We use new methods: cubic overestimation methods and then compare them with the damped Newton methods which are the current most popular methods. The former methods seem faster than the latter methods from the numerical results.
Mentor: Robert Lowrie