Asymptotic analysis of the spatial weights of the arbitrarily high order transport method
We perform an asymptotic analysis to the spatial weights of the Arbitrarily High Order Transport (AHOT) method that employs the method of characteristic as a means to relate the surface and the average fluxes of a computational cell in twodimensional Cartesian geometry. Previously, the spatial weights of the AHOT’s final discrete-variable equations have shown some numerical instabilities as the cell optical thickness approaches zero (or when computed on sufficiently thin cells). Our analysis is based on identifying the components of the spatial weights that are responsible for these instabilities, then expanding them in a truncated power series of the cell optical thickness that causes the instabilities when approaches zero. We then derive the conditions necessary to eliminate the singularity as the cell optical thickness approaches zero. We show that the method we adopted for computing the asymptotic spatial weights is very effective in eliminating these numerical instabilities by comparing the weights using the full analytical expressions and the new asymptotic ones, both being computed on fine grids. We implement the new asymptotic formulas for the spatial weights in the AHOT-C test code and generate benchmark quality solutions to some of the Burre’s Suite of Test Problems (BSTeP), which can be used as reference solutions to verify the accuracy of other solution methods and algorithms.