Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

Details Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

2006-12-12

arxiv.org/abs/math/0612324v1

Mathematics

Numerical Analysis

Scientific paper

10.1103/PhysRevE.76.016708

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 CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm.

Affiliated with

Also associated with

No associations

Rating

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585822