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MMS3D is a program for creating method of manufactured solutions with escalating order of non-smoothness for the one-group SN equations in a homogeneous domain. The smoothness of the manufactured solution is set by boundary conditions that can be specified in the input file as polynomials. The boundary conditions and a uniform auxiliary source Q are used to compute the analytical angular flux solution for a problem without scattering. This solution is the manufactured solution. For using it in problems with scattering, the scattering cross section is set and a distributed source q is computed such that the solution to the SN equation with scattering is the previously computed angular flux. The code computes reference solutions for Cartesian meshes. It does so by computing the Legendre polynomial moments of the angular flux solution, scalar flux solutions, distributed source, and inflow boundary fluxes for each cell and relevant face.
The reference solution is available in analytical form. The Legendre moments of the angular flux, scalar flux, distributed source and inflow boundary fluxes are integrated analytically from these expressions. For this purpose, the singular characteristic line and the singular planes have to be tracked through the Cartesian geometry. On each side of the singular planes distinct analytical expressions of the solution and sources are presents so in elements intersected by the singular planes, the contributions to the integral over the elements must be accumulated separately. More details of the computational algorithm are included in the theory references that are included with the code.
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Keywords: SN method, algorithms, deterministic method, finite element method, numerical solution, radiation transport.