An accurate and scalable direction-splitting solver for flows laden with non-spherical rigid bodies—Part 2: Moving rigid bodies

Abstract

The Direction Splitting algorithm is a computational method that facilitates the solution of the Navier–Stokes equation by decomposing a multi-dimensional Poisson equation into a series of one-dimensional equations. This approach allows for efficient and scalable numerical computations. The incorporation of rigid bodies in the computational domain is made possible by modifying the diffusion and divergence stencils near the fluid–solid interface. In our recent study (Goyal and Wachs, 2023), we implemented stencil corrections for fixed non-spherical rigid bodies and demonstrated the scalability and accuracy of the DS algorithm for a wide range of test cases. This study presents an extension of the Direction Splitting solver to effectively compute the dynamics of moving non-spherical rigid bodies in the presence of fluid flow. The interaction between rigid bodies and fluid can be categorized as either one-way or two-way coupled. The stencils resolving the fluid–solid interface are updated at every time-iteration to account for changes in particle position and orientation. We demonstrate that the adaptation of the diffusion and divergence stencil in the literature (Goyal and Wachs (2023); Keating and Minev (2013)) is inadequate for accurately predicting the dynamics of moving rigid bodies in a two-way coupled simulation, especially at O(102) Reynolds number. Hence, we implement a conservative cut-cell method for the discretization of the divergence term, and we also take into account the proximity of the fluid–solid interface in the advection discretization. The results of multiple test cases demonstrate that the suggested stencil modifications effectively capture the dynamics of fluid flow in the presence of freely moving rigid bodies. However, the cut-cell discretization of the divergence term constitutes a significant computing overhead that impacts the fast computing property of the Direction Splitting algorithm.