I am following the work of Lee and Lin ( JCP 2005 ) to study droplet dynamics. I am having problem in implementing the Nuemann wall boundary condition. How to implement this boundary condition ? Should it be applied to all the derivatives of density normal to the wall boundary ? How to implement this condition for solving the Laplacian of density to calculate the chemical potential using isotropic derivatives ?
It would be very helpful if anybody can help me in this regard.
Have you solved your problem? If so, I’d like to know what you have done.
I have been looking at the following papers…
Taehun Lee and Lin Liu ,PHYSICAL REVIEW E 78, 017702 2008, Wall boundary conditions in the lattice Boltzmann equation method for nonideal gases
Kevin Connington, Taehun Lee, Journal of Computational Physics 250 (2013), Lattice Boltzmann simulations of forced wetting transitions
of drops on superhydrophobic surfaces
Taehun Lee, Lin Liu, Journal of Computational Physics 229 (2010), Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces
I will be implementing the BCs with the HeLee dynamics.
I have not yet figured out the implementation for contact angle. I will be working on it a bit later this year. Let me know if you have got some results.