Diffusion Synthetic Acceleration of S{sub n} Linear Nodal Schemes in Weighted Difference Form
The consistent formulation of a diffusion synthetic acceleration (DSA) equation, which is derived directly from the discretized form of a transport equation following the methods of Alcouffe and Larsen, encounters problems in practical application to the higher-order multidimensional differencing schemes due to the relatively complex form of the resulting equation and to the difficulties in solving it efficiently. Alternative approaches, like the method of Khalil, in which the starting point is the continuous transport equation, or that of Azmy, in which the cell-centered discretization is used, yield DSA equations in a form much easier to solve. Several authors have developed transport-based synthetic acceleration methods, in which the acceleration equation is derived directly from a discretized transport equation and can be solved efficiently with minimal programming effort. However, for diffuse-mode-dominated problems, the use of transport acceleration may not be the optimal solution because the diffusion equation can be solved faster. Azmy has shown that arbitrarily high-order multidimensional nodal methods can be cast in a weighted-difference form that is suitable for the formulation of a DSA algorithm. The stability and convergence of such a DSA scheme has been proved for the lowest-order nodal method, i.e., constant-surface flux, but no attempt has been made to apply this algorithm to higher-order differencing schemes. Here, we describe the implementation of DSA to the linear (LN) and bilinear (BL) nodal approximations taking into account linearly isotropic scattering. We have implemented consistently formulated DSA equations for multidimensional nodal methods in weighted-difference form. The final acceleration equation retains a relatively simple form of interface current equations with matrices that are inexpensive to compute. Further work is needed for more efficient methods to solve the DSA equation. The preliminary results of the implementations of the multigrid methods to solve the acceleration equation are encouraging.
- Research Organization:
- Commissariat a l'Energie Atomique (FR)
- Sponsoring Organization:
- none (US)
- OSTI ID:
- 786748
- Report Number(s):
- none; ISSN 0003-018X; CODEN TANSAO; ISSN 0003-018X; CODEN TANSAO
- Country of Publication:
- United States
- Language:
- English
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