COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
- Research Organization:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- Sponsoring Organization:
- DOE - NE
- DOE Contract Number:
- DE-AC07-05ID14517
- OSTI ID:
- 1016189
- Report Number(s):
- INL/CON-11-21643; TRN: US201112%%253
- Resource Relation:
- Conference: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Eng,Rio de Janeiro, Brazil,05/08/2011,05/12/2011
- Country of Publication:
- United States
- Language:
- English
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