Algorithm refinement for stochastic partial differential equations.

Conference · Mon Jan 01 04:00:00 EST 2001

DOI:https://doi.org/10.1063/1.1581638· OSTI ID:975926

Alexander, F J ^[1]; Tartakovsky, D M ^[2]

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1. Francis J.
2. Daniel M.

A hybrid particle/continuum algorithm is formulated for Fickian diffusion in the fluctuating hydrodynamic limit. The particles are taken as independent random walkers; the fluctuating diffusion equation is solved by finite differences with deterministic and white-noise fluxes. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass conservation. This methodology is an extension of Adaptive Mesh and Algorithm Refinement to stochastic partial differential equations. A variety of numerical experiments were performed for both steady and time-dependent scenarios. In all cases the mean and variance of density are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the mean density is correct, but the variance is reduced except within the particle region, far from the interface. Extensions of the methodology to fluid mechanics applications are discussed.

• Research Organization: Los Alamos National Laboratory
• Sponsoring Organization: DOE
• OSTI ID: 975926
• Report Number(s): LA-UR-01-6964
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
DIFFUSION
DIFFUSION EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
MESH GENERATION
PARTIAL DIFFERENTIAL EQUATIONS