Algorithm refinement for stochastic partial differential equations: II. Correlated systems

Journal Article · Wed Aug 10 04:00:00 EDT 2005 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2005.02.004· OSTI ID:20687250

Alexander, Francis J ^[1]; Garcia, Alejandro L ^[2]; Tartakovsky, Daniel M ^[3]

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1. CCS-3, Los Alamos National Laboratory, MS-B256, Los Alamos, NM 87545 (United States)
2. Department of Physics, San Jose State University, San Jose, CA 95192-0106 (United States)
3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia, D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.

• OSTI ID: 20687250
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 207; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CORRELATIONS
DENSITY
DIFFUSION
FLUCTUATIONS
GASES
HYBRIDIZATION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
RANDOMNESS
TRANSPORT THEORY
VELOCITY