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Updated: Jul 13, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations
John B Bell1, Alejandro L Garcia, Sarah A Williams
1Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Summary
A new numerical scheme accurately models thermal fluctuations in fluid dynamics using Landau-Lifshitz Navier-Stokes (LLNS) equations. This method improves upon existing computational fluid dynamics approaches for energy and density fluctuations.
Area of Science:
- Computational physics
- Fluid dynamics
- Statistical mechanics
Background:
- The Landau-Lifshitz Navier-Stokes (LLNS) equations describe hydrodynamics with thermal fluctuations.
- Existing computational fluid dynamics (CFD) schemes struggle to accurately capture these fluctuations.
Purpose of the Study:
- To evaluate explicit Eulerian discretizations of the LLNS equations.
- To develop an accurate numerical method for simulating thermal fluctuations in fluids.
Main Methods:
- Examined MacCormack's two-step Lax-Wendroff and piecewise parabolic methods.
- Introduced and tested a conservative centered scheme with a third-order Runge-Kutta integrator.
- Compared results with theoretical predictions and direct simulation Monte Carlo (DSMC) methods.
Main Results:
- Existing CFD schemes accurately modeled momentum fluctuations but not energy or density.
- The new conservative centered scheme accurately reproduced fluctuations in density, energy, and momentum.
- Numerical tests, including a random walk of a shock wave, validated the new solver.
Conclusions:
- A novel conservative centered scheme provides accurate simulations of thermal fluctuations in hydrodynamics.
- This method advances the computational modeling of stochastic fluid behavior.
- The findings offer improved tools for studying complex fluid phenomena.
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