Dear Debashis,

The main idea of EDM, when compared to standard forcing schemes, is to remove the dependence of the forcing term on the kinematic viscosity. You can appreciate the improvement at small relaxation times, while when tau=1 the method is equivalent to standard forcing.

I suggest you to take a look at my papers

1) Numerical Simulation of Diffusion Process in T-shaped Micromixer using Shan-Chen Lattice Boltzmann Method

2) Numerical simulation of the collision of two microdroplets with a pseudopotential multiple-relaxation-time lattice Boltzmann model

In both cases I used EDM, in combination with Shan-Chen model and, in the second paper, with MRT. I hope they will help.

Best Regards,

Ernesto

I totally agree with Ernesto Monaco and the information stated in his well-written papers.

To lighten the notation, let us implicilty assume the dependence on space and time in the following. Let us consider a certain body force $\bm{F}$. The exact difference method [1] suggests to correct the post-collision populations by adding a forcing term $\mathcal{F}_i$ defined as

\begin{equation}

\mathcal{F}_i = f_i^{eq}(\rho, \bm{u}+\Delta \bm{u})-f_i^{eq}(\rho, \bm{u}).

\end{equation}

In other words, $\mathcal{F}_i$ is the difference in local equilibrium distribution functions between the fluid at a velocity increased by $\Delta \bm{u} = \frac{\bm{F} \Delta t}{\rho}$ and the fluid at its actual velocity.

[1] Kupershtokh, A. L., & Medvedev, D. A. (2006). Lattice Boltzmann equation method in electrohydrodynamic problems. Journal of Electrostatics, 64(7-9), 581-585.

Dear Debashis Panda,

You can find the basic assumption and the way of derivation of the EDM in this paper:

"Introducing a modified exact difference method for incorporating unsteady and non-uniform force terms in lattice kinetic models".

To those reading this thread. Kuperhstokh's EDM suggested by Ernesto Monaco does not "remove the dependence of the forcing term on the kinematic viscosity". Although the original formulation of the EDM does not contain a viscosity-related variable, this does not mean that EDM is viscosity-independent. We recently published an article which proves and numerically demonstrates that EDM does introduce a viscosity dependence. (Force methods for the two-relaxation-times lattice Boltzmann)