Toward a discrete maximum principle for the implicit Monte Carlo equations
- Los Alamos National Laboratory
It has long been known that temperature solutions of the Implicit Monte Carlo (IMC) equations can exceed the external boundary temperatures, a so-called violation of the 'maximum principle.' Previous attempts at prescribing a maximum value of the time step size {Delta}{sub t} that is sufficient to eliminate these violations have recommended a {Delta}{sub t} that is typically too small to be used in practice and that appeared to be much too conservative when compared to numerical solutions of the IMC equations for practical problems. In this paper, we derive a new estimator for the maximum time step size that includes the spatial grid size {Delta}{sub x}. This explicitly demonstrates that the effect of coarsening {Delta}{sub x} is to increase the limit on {Delta}{sub t}, which helps explain the overly conservative nature of the earlier, grid-independent results. As {Delta}{sub x} is reduced to zero, the original result due to Larsen and Mercier is almost reproduced (the discrepancy is also explained). We demonstrate that our new time step restriction is a much more accurate means of producing violations of the maximum principle. We discuss how the implications of the new time step restriction can impact IMC codes.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1043451
- Report Number(s):
- LA-UR-10-08114; LA-UR-10-8114; TRN: US201214%%8
- Resource Relation:
- Conference: NECDC 2010 ; October 18, 2010 ; Los Alamos, NM
- Country of Publication:
- United States
- Language:
- English
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