Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations
We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation of the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 1188925
- Report Number(s):
- PNNL-SA-107019; KJ0401000
- Journal Information:
- Journal of Chemical Physics, 141(22):224112, Journal Name: Journal of Chemical Physics, 141(22):224112
- Country of Publication:
- United States
- Language:
- English
Similar Records
Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations
Contribution to Von Karman Institute lecture series on ''Computational Fluid Dynamics'': advection-diffusion and Navier-Stokes equations