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Algorithm Refinement for Stochastic Partial Differential Equations: I. Linear Diffusion
Journal of Computational Physics (2002)
  • Alejandro Garcia, San Jose State University
  • Francis Alexander, Los Alamos National Laboratory
  • Daniel Tartakovsky, Lawrence Livermore National Laboratory
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. Results from a variety of numerical experiments are presented 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 nonstochastic version (i.e., using only deterministic continuum fluxes) the mean density is correct, but the variance is reduced except in particle regions away from the interface. Extensions of the methodology to fluid mechanics applications are discussed.
  • linear diffusion,
  • algorithm refinement
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Citation Information
Alejandro Garcia, Francis Alexander and Daniel Tartakovsky. "Algorithm Refinement for Stochastic Partial Differential Equations: I. Linear Diffusion" Journal of Computational Physics Vol. 182 (2002)
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