Applied Mathematics and Plasma Physics

F. J. Alexander, A. L. Garcia and D. M. Tartakovsky, "Algorithm refinement for stochastic partial differential
equations: II. Correlated systems", *J. Comp. Phys.*, vol. 207, no. 2, pp. 769-787, 2005

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 [J. Comp. Phys. 182 47 (2002)]. 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 nonstochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.

@article{alexander-2005-algorithm,

author = {F. J. Alexander and A. L. Garcia and D. M. Tartakovsky},

title = {Algorithm refinement for stochastic partial differential
equations: II. Correlated systems},

year = {2005},

urlpdf = {http://math.lanl.gov/~dmt/papers/alexander-2005-algorithm.pdf},

journal = {J. Comp. Phys.},

volume = {207},

number = {2},

pages = {769-787}

}