Coarse mesh transport theory model for heterogeneous systems

To improve fuel utilization, recent reactor cores have become substantially more heterogeneous. In these cores, use of variable fuel enrichments and strong absorbers lead to high neutron flux gradients, which may limit the accuracy (validity) of diffusion theory based methods. In fact, the diffusion equation itself may become a poor approximation of the Boltzmann equation, the exact equation that describes the neutron flux. Therefore, numerical methods to solve the transport equation efficiently over a large heterogeneous region (such as a reactor core) are very desirable in case where the diffusion approximation breaks down.; Presently, the only methods capable of computing the power (flux) distributions very accurately throughout a large system such as a nuclear reactor core are the Monte-Carlo or the fine-mesh transport theory methods. Both these methods suffer from the long computational time which makes them useless for routine core calculations.; Starting from a variational principle that admits trial functions that can be discontinuous at coarse mesh (assembly) interfaces, we propose a method to solve the transport equation on a spatial grid made up of meshes as large as the size of a fuel assembly. The variational principle is derived for the most general case, but further methods are developed for one-dimensional geometry with the angular variable treated by discrete ordinates.; The method uses the finite element approach for the space variable with basis functions precomputed for each element to obtain an algebraic linear system of equations. The eigenvalue of this system is the multiplication constant and the eigenvector represents the incoming angular fluxes for each coarse mesh. The latter allows the reconstruction of the fine mesh solution (angular flux) throughout the domain of interest when used with the basis functions (surface Green's function) for each coarse mesh. The method requires no homogenization procedure that can be a serious source of errors. It reproduces the fine mesh discrete ordinates results at a fraction of the computational time. The new method is an extension of a previous work of Nichita and Rahnema for the diffusion equation.