An adaptive alpha for the implicit Monte Carlo equations
- Los Alamos National Laboratory
During the derivation of Fleck and Cumming's Implicit Monte Carlo (IMC) equations, a global user parameter {alpha} is introduced that may be adjusted in the range 0.5 {<=} {alpha} {<=} 1.0 in order to control the degree of 'implicitness' of the IMC approximation of the thermal radiative transfer equations. For linear (and certain nonlinear) problems, it can be shown that the IMC equations are second-order accurate in the time step size {Delta}{sub t} if {alpha} = 0.5, and they are first-order accurate otherwise. However, users almost universally choose {alpha} = 1 in an attempt to avoid unphysical temperature oscillations that can occur for problem regions in which the optical time step is large. In this paper, we provide a mathematically motivated, adaptive value of {alpha} that dynamically changes according to the space- and time-dependent problem data. We show that our {alpha} {yields} 0.5 in the limit of small {Delta}{sub t}, which automatically produces second-order accuracy. In the limit of large time steps, {alpha} > 1; this retains the 'fully implicit' time behavior that is usually employed throughout the entire problem. An adaptive {alpha} also has the advantages of being trivial to implement in current IMC implementations and allowing the elimination of a user input parameter that is a potential source of confusion. Test problems are presented to demonstrate the accuracy of the new approach.
- Research Organization:
- Los Alamos National Laboratory (LANL)
- Sponsoring Organization:
- DOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1043450
- Report Number(s):
- LA-UR-10-08113; LA-UR-10-8113
- Country of Publication:
- United States
- Language:
- English
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