Asymptotic derivation of the time-dependent SP[sub 2] equations and numerical calculations
- Los Alamos National Laboratory, NM (United States)
Converting the independent variables of the transport equation to dimensionless parameters, asymptotic analyses can be performed to show that for an important class of problems, the diffusion equation is an asymptotic limit of the transport equation. A recent paper by Larsen et al. provides a broadened view of the aforementioned result. It deals with the steady state transport equation and shows that the simplified spherical-harmonics (SP[sub N]) equations are robust high-order asymptotic approximations of the transport equation in a physical regime in which the conventional diffusion equation is the leading-order approximation. According to the reported numerical results for the steady-state cases for many problems, low-order SP[sub N] equations capture most (Gamino reports [open quotes]greater than 80%[close quotes]) of the transport corrections to the diffusion approximation. Tomasevic and Larsen show that in nearly all cases, the SP[sub 2] results are significantly more accurate than diffusion results in the steady-state problems. In this paper, we deal with the time-dependent transport equation using conventional asymptotic approaches and find that the time-dependent SP[sub 2] equations have the same asymptotic approximations as the time-dependent transport equation up to the third order in a physical regime in which the time-dependent diffusion equation is the leading-order approximation. In addition, we follow the same asymptotic approaches as Larsen et al. and find that if one neglects the time derivative term of the second moment of angular flux [partial derivative][psi][sub 2]/[partial derivative]t in the time-dependent SP[sub 2] equations, an equation is obtained that is identical to the third-order asymptotic approximation of the time-dependent transport equation (we will call this equation the modified time-dependent SP[sub 2] equation).
- OSTI ID:
- 6836975
- Report Number(s):
- CONF-931160-; CODEN: TANSAO
- Journal Information:
- Transactions of the American Nuclear Society; (United States), Vol. 69; Conference: American Nuclear Society (ANS) winter meeting, San Francisco, CA (United States), 14-18 Nov 1993; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
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