Kinetic modeling of immersed boundary layer for accurate evaluation of local surface stresses and hydrodynamic forces with diffuse interface immersed boundary method

Abstract

The motivation of this paper is to examine the evaluation of local surface stresses and hydrodynamic forces acting on a stationary or moving body using a diffuse interface immersed boundary method (IBM). This task is not trivial for the diffuse IBM because it uses a smoothed regularized delta function in the transfer steps between Lagrangian and Eulerian locations. In our earlier work [D. Xu et al., Phys. Rev. E 105, 035306 (2022)], a particle distribution function (PDF) discontinuity-based kinetic immersed boundary method (KIBM) was proposed based on the Boltzmann equation. This paper is a continuation of our work on the improvement of the KIBM in the framework of the diffuse interface IBM. In the present study, the concept of the immersed boundary layer (IBL) is brought forward, and the dynamic effects of particle advection and collision in the IBL are coupled and evaluated within a numerical time step scale in a kinetic manner. Consequently, the PDFs on both sides of the IBL are reconstructed, and the general immersed boundary force density can be obtained accurately and efficiently. Meantime, the local surface stress distribution acting on the body wall from the actual fluid can be conveniently and accurately calculated by the moment of the PDFs. Finally, some commonly used problems involving incompressible fluid flows in the continuum flow regime with stationary and moving boundaries are simulated by the present KIBM, and the results show that the present KIBM can significantly accelerate the rate of convergence and has a good agreement with other numerical and experimental results.