New Numerical Solution with the Method of Short Characteristics for 2-D Heterogeneous Cartesian Cells in the APOLLO2 Code: Numerical Analysis and Tests

The method of short characteristics is extended to two-dimensional heterogeneous Cartesian cells. The new application is intended for realistic pin-by-pin lattice calculations with an exact representation of the geometric shape of the pins, without need for homogenization. The method keeps the advantages of conventional discrete ordinates methods, such as fast execution, together with the possibility to deal with a large number of spatial meshes. Expansion bases, spatial integration, and balance conservation are discussed. A Fourier analysis of the method shows that the scheme preserves the asymptotic behavior of analytical transport. Two coarse-mesh finite difference acceleration techniques have also been analyzed and generalized with the use of Eddington's factors to speed up the rate of convergence of the inner iterations. Numerical examples for realistic configurations show the precision of the method and the efficiency of the accelerated iterations. An analytical stability analysis is also presented for studying the nonconverged behavior of the accelerated scheme, and we give numerical proof of chaotic behavior and the existence of bifurcations.