ALE Numerical Simulation for a Rigid Body Rotation About a Fixed Axis in a Incompressible Viscous Fluid

An efficient numerical method is presented in this paper. It combines a unique ALE formulation with an adaptive time algorithm based on a Courant-Friedrichs-Levy (CFL) type condition to simulate fluid and rigid body interactions. The ALE differential formulation includes the geometric conservation law (GCL) which has the mesh velocity as a variable. In the adaptive time algorithm, the time step selection is based on the CFL type condition which is estimated by the difference between the fluid and mesh velocity. With the adaptive algorithm, the numerical simulations of incompressible viscous flow around moving bodies when the motion of the bodies is not known in advance are stable. To validate the proposed method, only the body rotation about a fixed axis in a incompressible viscous fluid is considered because it causes the large deformation of mesh. The harmonic and damped vibrations of a physical pendulum in the air are tested and the opening of a swing check valve plate is simulated to determine its local resistance characteristics in comparison with experimental data. The numerical simulations show that when a rigid body rotates in an incompressible fluid, the distortion of the mesh element is not significant and the numerical results agree with the experimental data.