scholarly journals Simulation of Liesegang Pattern Formation Using Lattice Boltzmann Method in three Dimensions

2012 ◽  
Author(s):  
Wei Qiang ◽  
Hui Cao
Keyword(s):  
Pattern Formation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensions ◽  
Boltzmann Method

Enslaved Phase-Separation Fronts and Liesegang Pattern Formation

2011 ◽  
Vol 9 (5) ◽  
pp. 1081-1093 ◽  
Author(s):  
E. M. Foard ◽  
A. J. Wagner
Keyword(s):  
Phase Separation ◽  
Pattern Formation ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Critical Value ◽  
Exact Form ◽  
Analytical Derivation ◽  
Boltzmann Method

AbstractWe show that an enslaved phase-separation front moving with diffusive speeds can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

Two Phase Flow Simulation With Lattice Boltzmann Method: Application to Wave Breaking

2013 ◽  
Author(s):  
Amir Banari ◽  
Stephan T. Grilli ◽  
Christian F. Janssen
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Wave Breaking ◽  
Fluid Pressure ◽  
High Density ◽  
Three Dimensions ◽  
Breaking Wave ◽  
Computational Domain ◽  
Density Ratios ◽  
Boltzmann Method

A new Lattice Boltzmann method (LBM) is developed to efficiently simulate multiphase flows with high density ratios, in order to study complex air-sea interaction problems, such as wind wave breaking and related sea-spray generation. In this method, which builds and improves on the method proposed earlier by [1], the motion of (diffusive) interfaces between fluids is modeled by solving the convective Cahn-Hilliard equation with the LBM. As in the latter work, we eliminate instabilities resulting from high density ratios by solving an additional Poisson equation for the fluid pressure. The resulting numerical scheme is computationally demanding since this equation must be solved over the entire computational domain, which motivates implementing the method on the massively parallel environment offered by General Purpose Graphical Processing Units (GPGPU), via the nVIDIA CUDA framework. In this paper, we present the equations and numerical methods for the method and the initial validation of the resulting multiphase-LBM for standard benchmark problems such as Poiseuille flow, a rising bubble, and Rayleigh-Taylor instability for two-fluid systems. A good agreement with the reference solutions is achieved in all cases. Finally, the method is applied to simulating an ocean breaking wave in a space periodic domain. In all the presented applications, it is observed that the GPGPU implementation leads to speed-ups of about two orders of magnitude in comparison to a single-core CPU implementation. Although the method is only currently implemented in a two-dimensional (2D) framework, its extension to three-dimensions (3D) should be straightforward, but the need for the efficient GPGPU implementation will become even more drastic in 3D.

scholarly journals Lattice-Boltzmann method applied to the pattern formation on periodic surface structures generated by multiline nanosecond laser

DYNA ◽  
2014 ◽  
Vol 81 (187) ◽  
pp. 108-114
Author(s):  
Frank Rodolfo Fonseca-Fonseca ◽  
José Edgar Alfonso-Orjuela ◽  
Darío Fernando Andrade
Keyword(s):  
Pattern Formation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Surface Structures ◽  
Nanosecond Laser ◽  
Periodic Surface ◽  
Boltzmann Method
Sign in / Sign up

Export Citation Format

Share Document