Spectral analysis of numerical methods for discrete-ordinates problems. I
A separation of variables method is proposed for the analysis of spatial differencing schemes for discrete-ordinates problems. This method leads to the definition of a ''spectrum'' for the differencing scheme which is a function of the cross sections and the spatial mesh. An analysis of the spectrum as a function only of the mesh yields theoretical results regarding stability, positivity, and accuracy which have not been obtained previously. In this paper, we apply the theory to the standard diamond difference scheme and a new extended diamond difference scheme. Numerical results obtained from the solution of discrete-ordinates problems using these two schemes are shown to be in excellent agreement with the spectral theory.
- Research Organization:
- University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
- OSTI ID:
- 5871918
- Journal Information:
- Transp. Theory Stat. Phys.; (United States), Vol. 15:1
- Country of Publication:
- United States
- Language:
- English
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