THE ANALYTICAL SOLUTION TO THE MULTIGROUP DIFFUSION EQUATION IN ONE-DIMENSIONAL PLANE, CYLINDRICAL AND SPHERICAL GEOMETRIES

摘要

By viewing the multigroup diffusion equation in plane, cylindrical and spherical geometries as matrix equations, standard solution techniques for second order ordinary differential equations can be applied to find analytical solutions. By adjusting the boundary conditions appropriately, a solution with the simplicity of the one-group case in the three geometries is found. Diffusion in cylindrical geometry is used as a demonstration of critical and fixed source problems. No special considerations are required when fission is present or not in any region. The solution is new, and, because of its generality, completely eliminates the need for numerical multigroup solutions of the diffusion equation in heterogeneous plane, spherical and cylindrical geometries.