Lattice Boltzmann immiscible two-phase model (LBM)

Starting point for newcomers wanting to study RK-type lattice Boltzmann immiscible two-phase model.

This code may be use as a starting point for newcomers wanting to study RK-type lattice Boltzmann immiscible two-phase model. It may give a better understanding of the RK-type lattice Boltzmann two-phase model.
This m-code reproduces some of the results of Table 3 in section 3.2 "Steady Bubble" of the following reference:
R1) Leclaire, S., Reggio, M. and Trépanier, J.-Y. (2012). Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model, Applied Mathematical Modelling 36(5): 2237-2252.

The results are stored in the file "results.txt". The code "main.m" will take several hours to complete all simulations.

Moreover, instead of using the second order non-isotropic color gradient, it is possible to use isotropic color gradient of the following reference:
R2) Leclaire, S., Reggio, M. and Trépanier, J.-Y. (2011). Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model, Computers and Fluids 48(1): 98-112.

In average, results are better with the isotropic discretisation.

If these m-files were useful in your work, please cite:
1) The above two references R1 and R2 accordingly.

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If you have downloaded these m-files, the following references could also be of interest:

Generalization of this model to multiple immiscible components:
R3) Leclaire, S., Reggio, M. and Trépanier, J.-Y. (2013) Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios. Journal of computational physics 246: 318-342.

Additional terms for modeling variable density ratios:
R4) Leclaire, S., Pellerin, N., Reggio, M. and Trépanier, J.-Y. (2013) Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models. International Journal of Multiphase Flow 57: 159-168.

Introduction of MRT and model validation for simulating unsteady multiphase flows:
R5) Leclaire, S., Pellerin, N., Reggio, M. and Trépanier, J.-Y. (2014) Unsteady immiscible multiphase flow validation of a multiple-relaxation-time lattice Boltzmann method. Journal of Physics A: Mathematical and Theoretical 47(10): 105501.

Introduction of the cascaded collision (with unit density ratio):
R6) Leclaire, S., Pellerin, N., Reggio, M. and Trépanier, J.-Y. (2014) Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications 406: 307-319.

Others related publications may be found there:
http://scholar.google.ca/citations?user=_wUUbqwAAAAJ&hl=en