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

• Lees–Edwards boundary condition (LEBC) is used to introduce shear into region.
• LEBC is combined with smoothed profile method to eliminate Galilean invariance error.
• Using the combined method, the particle vertical velocity stays constant.
• There are some bumps in the angular velocity using first-order interpolation.
• Third interpolation removes bumps in angular velocity of boundary-crossing particle.

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.

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