Mathematical and computational framework for moving and colliding rigid bodies in a Newtonian fluid

Abstract

We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To model the interactions between bodies, we consider a repulsive collision-avoidance model, defined by R. Glowinski. The main emphasis in this work is the generalization of this collision model to multiple rigid bodies of arbitrary shape. Our model first uses a narrow-band fast marching method to detect the set of colliding bodies. Then, collision forces and torques are computed for these bodies via a general expression, which does not depend on their shape. Numerical experiments examining the performance of the narrow-band fast marching method and the parallel execution of the collision algorithm are discussed. We validate our model with literature results and show various applications of colliding bodies in two and three dimensions. In these applications, the bodies move due to forces such as gravity, a fluid flow, or their own actuation. Finally, we present a tool to create arbitrarily shaped bodies in discretized fluid domains, enabling conforming body-fluid interface and allowing to perform simulations of fluid-body interactions with collision treatment in these realistic environments. All simulations are conducted with the Feel++ open source library.

Figures (11)

• Figure 1: Evolution of the vertical position of mass center, vertical translational velocity, Reynolds number and translational kinetic energy. The red line are the present results, the green dotted and blue dotted lines correspond to results respectively taken from wang_drafting_2014 and wan_direct_2006. The streamlines and body position at four different time instants are represented.
• Figure 2: Comparison of the vertical position of the center of mass and vertical translational velocity observed in present results, red line, to literature results zamora_numerical_2019, dotted line.
• Figure 3: The left graph plots the trajectory of the ellipse center of mass. The red line corresponds to the present results and the blue dotted line represents the literature results xia_flow_2009. The right graph shows the same trajectory but compares it to rotations happening on the other wall.
• Figure 4: Evolution of the horizontal position of the center of the ellipsoid. The dotted line shows the literature results pan_direct_2002 and the red line represents the present results.
• Figure 5: The upper figures show the position of the two disks as well as the streamlines at four different time instants. The lower graphs compare the evolution of the disks horizontal and vertical position to literature feng_immersed_2004. The solid lines correspond to present results and the dotted one to literature results.