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Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations
Physical Review (2007)
  • Alejandro Garcia, San Jose State University
  • John B Bell, Lawrence Berkeley National Laboratory
  • Sarah Williams, 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.
  • numerical methods,
  • strokes,
  • equations
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Alejandro Garcia, John B Bell and Sarah Williams. "Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations" Physical Review Vol. E 76 (2007)
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