# Lattice-Boltzmann-Langevin simulations of binary mixtures.

@article{Thampi2011LatticeBoltzmannLangevinSO, title={Lattice-Boltzmann-Langevin simulations of binary mixtures.}, author={Sumesh P. Thampi and Ignacio Pagonabarraga and R. Adhikari}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2011}, volume={84 4 Pt 2}, pages={ 046709 } }

We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation… Expand

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#### References

SHOWING 1-10 OF 126 REFERENCES

Thermal fluctuations in the lattice Boltzmann method for nonideal fluids.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is demonstrated that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long-wavelength limit using the lattice Boltzmann method. Expand

Fluctuating lattice Boltzmann

- Physics
- 2005

The lattice Boltzmann algorithm efficiently simulates the Navier-Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to… Expand

Statistical mechanics of the fluctuating lattice Boltzmann equation.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2007

A derivation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statistical mechanics and fluctuating hydrodynamics is proposed and believes this formalism will be useful in developing new algorithms for thermal and multiphase flows. Expand

Fluctuating dynamics of nematic liquid crystals using the stochastic method of lines.

- Physics, Medicine
- The Journal of chemical physics
- 2010

This work constructs Langevin equations describing the fluctuations of the tensor order parameter Q(alphabeta) in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de Gennes free energy and demonstrates excellent agreement between numerics and theory. Expand

NUMERICAL SIMULATIONS OF PARTICULATE SUSPENSIONS VIA A DISCRETIZED BOLTZMANN EQUATION: PART 1. THEORETICAL FOUNDATION

- Physics
- 1993

A new and very general technique for simulating solid-fluid suspensions is described ; its most important feature is that the computational cost scales linearly with the number of particles. The… Expand

Fluctuating fluid interfaces.

- Physics, Medicine
- Physical review letters
- 1995

Both the equilibrium behavior and the roughening of the simulated interface is found to be in good agreement with theory over a remarkably large range of length and time scales. Expand

Lattice-Boltzmann Method for Complex Flows

- Computer Science
- 2010

This work reviews many significant developments over the past decade of the lattice-Boltzmann method and discusses higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Expand

Discrete solution of the electrokinetic equations.

- Chemistry, Physics
- The Journal of chemical physics
- 2004

A robust scheme for solving the electrokinetic equations is presented, combining the lattice-Boltzmann method with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. Expand

Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study

- Physics
- Journal of Fluid Mechanics
- 2001

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamically consistent lattice Boltzmann method.… Expand

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales

- Mathematics, Computer Science
- J. Comput. Phys.
- 2007

The theoretical analysis and numerical results show that the immersed boundary method with thermal fluctuations captures many important features of small length scale hydrodynamic systems and holds promise as an effective method for simulating biological phenomena on the cellular and subcellular length scales. Expand