Projected Discrete Ordinates Methods for Numerical Transport Problems

A class of “projected discrete ordinates” (PDO) methods is described for obtaining iterative solutions of discrete ordinates problems with convergence rates comparable to those observed using diffusion synthetic acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the choice of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented that illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.