Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations

Bell, John B.; Garcia, Alejandro L.; Williams, Sarah A.

doi:10.1103/PhysRevE.76.016708

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations

Journal Article · Thu Jul 26 04:00:00 EDT 2007 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.76.016708· OSTI ID:924374

Bell, John B. ^[1]; Garcia, Alejandro L.; Williams, Sarah A.

University of California, Davis

The Landau-Lifshitz Navier-Stokes LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Research Organization:: Univ. of California (United States)

Sponsoring Organization:: USDOE - Office of Science (SC)

DOE Contract Number:: FC02-01ER25473

OSTI ID:: 924374

Report Number(s):: DOE-UCDAVIS-25473-09

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 1 Vol. 76; ISSN 1539-3755; ISSN PLEEE8

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

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