The Mirroring Immersed Boundary Method - Modeling Fluids with Moving and Interacting Bodies

Doctoral thesis, 2008

The detailed fluid flow around arbitrary, moving, interacting and deforming bodies is both complex and poorly understood and the commercial simulation tools simulating such flows are computationally to demanding. Hence, a new fast and accurate method for simulating complex multi-body flows is required. This thesis derives, implements and validates two implicit second-order accurate simulation methods that simulate the complex flow around multiple immersed bodies. In the methods the fluid velocity is constrained by an implicit immersed boundary (IB) condition such that it exactly follows the IB, the boundary of the bodies. Two such conditions are developed, resulting in two different methods, the vertex constraining IB method, constraining the velocity at vertex control points defining the IB, and the mirroring IB method, mirroring the velocity field over the IB. Both methods account for the presence of the IB in the continuity equation. The bodies are moved as a result of the forces acting upon them, determined by integrating the pressure and the viscous forces over the body. The deformation of the bodies is modeled by the Euler-Bernoulli beam equation, and the body collisions are modeled by a proposed triangle-triangle collision force. The methods are validated by simulating an immersed sphere for a range of Reynolds numbers. For the mirroring IB method a convergence study is employed, that shows the superiority in the convergence rate compared to other IB methods. The mirroging IB method is validated for moving bodies by simulating sedimenting spherical bodies at low Reynolds numbers. The triangle-triangle collision force is validated by a head on collision, and the proposed fluid-structure interaction model is validated by simulating the cross flow over vertically aligned fibers. All validation cases are in good agreement with known theories, experiments or simulations, and grid refinement studies have been made to show the second-order accuracy.