Variational Integrators and Fluid‐Structure‐Interaction at Low Reynolds‐Number

Abstract

AbstractFor the special case of incompressible and highly viscous fluids, the interaction with a rigid body can be collected in a damping matrix, relating the velocities and angular velocities of the body with the fluid force and torque. This damping matrix (a.k.a. viscous resistance matrix) depends exclusively on the geometry and needs to be computed only once. We consider a rigid body moving in an unbound fluid. The generalized dissipative forces from the fluid onto the body enter the time discretization via the discrete D'Alembert Principle. As generally large rotations may occur, we chose quaternions for a singularity‐free description of the body orientation. The corresponding holonomic constraint of a unit quaternion is enforced on the position and momentum level by the RATTLE algorithm. The problem of Stokes drag on a sedimenting particle serves as an example.