EXPONENTIAL CHARACTERISTIC NONLINEAR RADIATION TRANSPORT METHOD FOR UNSTRUCTURED GRIDS OF TRIANGULAR CELLS

The exponential characteristic (EC) method is one of a family of nonli near spatial quadratures for discrete ordinates radiation transport th at are positive and at least second-order accurate and provide accurat e results for deep-penetration problems using coarse meshes. We use a split-cell methodology to adapt the method to unstructured grids of ar bitrarily shaped and oriented triangular cells that provide efficient representation of curved surfaces. Exponential representations of the flux entering through a cell edge and of the scattering source within a cell are constructed to match average values and first moments passe d form the adjacent cell (or from the boundary conditions) or obtained from the angular quadrature of the directional flux spatial moments i n the previous iteration (or from an initial guess). The resulting one - and two-dimensional nonlinear rootsolving problems are efficiently s olved using Newton's method with an accurate starting approximation. I mproved algorithms, presented here, have increased the efficiency of t he method by a factor of 10 as compared to an initial report. The EC m ethod now costs only twice as much per cell as does the linear charact eristic method but can be accurate with many fewer cells. Numerical te sting shows the EC method to be robust and effective.