Trans-Mesh Method and Its Application to Simulations of Incompressible Fluid-Rigid Bodies Interaction

In this paper, a Trans-mesh method is presented for simulating three-dimensional incompressible fluid-rigid body interaction with collisions. In the Trans-mesh method, the bodies can move freely in a main mesh that covers the entire flow field. The method is constructed based on the four-dimensional control volume in space-time unified domain such that the method assures to be divergence-free in the space-time unified domain and thus satisfies both the physical and geometrical conservation laws simultaneously. First of all, it is confirmed that the present method satisfies the geometric conservation law. Next, we did calculations for a single sphere settling under gravity in the stationary fluid to evaluate the present method. The method was applied to a flow around bodies driven by a flow in a square duct and the unsteady behavior of the flow is shown. The results indicate that this method is promising in such simulations.