Combining Lees–Edwards boundary conditions with smoothed profile-lattice Boltzmann methods to introduce shear into particle suspensions

Using walls to introduce shear into a domain causes wall effects in the calculation of rheological properties of suspensions. Employing Lees–Edwards boundary conditions as an alternative method, removes these effects. Earlier methods of solid–fluid interactions in the framework of lattice Boltzmann method, such as Ladd and ALD methods, violate conservation law of the translational and rotational momentum (Galilean invariance). In the present study, Lees–Edwards boundary condition has been combined with smoothed profile method (SPM) intending to eliminate Galilean invariance errors. The combined method is validated by allowing a particle to cross a Lees–Edwards boundary. Moreover, third-order interpolation is used for particle distribution functions leaving the domain in the velocity gradient direction to eliminate bumps in the angular velocity of the particle when crossing the Lees–Edwards boundary. As another test case, two interacting circular cylinders placed in a sheared domain using Lees–Edwards boundary condition. Comparing results with the ones presented in the literature shows good agreement.