Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Journal Article · Tue Jan 01 04:00:00 EST 2008 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.05.003· OSTI ID:956682

Densmore, Jeffery D ^[1]; Warsa, James S ^[1]; Lowrie, Robert B ^[1]; Morel, Jim E ^[2]

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1. Los Alamos National Laboratory
2. TEXAS A&M UNIV

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 956682
• Report Number(s): LA-UR-08-08070; LA-UR-08-8070
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 16 Vol. 228; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
COMPTON EFFECT
ENERGY DENSITY
FOKKER-PLANCK EQUATION
OSCILLATIONS
PHOTONS
SIMULATION
STABILITY
TEMPERATURE DEPENDENCE