Particle distribution function discontinuity-based kinetic immersed boundary method for Boltzmann equation and its applications to incompressible viscous flows

In this paper, a general immersed boundary force density is introduced for the Boltzmann equation and finally expressed as the desired particle distribution function discontinuity across the immersed boundary. Because of its independence of any specific boundary conditions and any specific solvers for the Boltzmann equation, it actually establishes a unified framework to incorporate various types of boundary conditions and several different kinds of solvers for the Boltzmann equation. Hence, a particle distribution function discontinuity-based kinetic immersed boundary method (KIBM) for the Boltzmann equation is proposed based on this general immersed boundary force density. Subsequently, this paper primarily focuses on the isothermal incompressible fluid-solid flows, and uses the discrete unified gas kinetic scheme to solve the Boltzmann Bhatnagar-Gross-Krook model equation. Meanwhile, the regularized delta function and the bounce-back rule combined with an iterative IBM correction procedure are employed in obtaining the general immersed boundary force density to enforce the no-penetration and no-slip boundary conditions on the solid wall. Finally, some numerical experiments for typical incompressible fluid-solid flows show that the present KIBM could provide good agreement with other numerical and experimental results.