An arbitrary lagrangian eulerian volume of fluid method for floating body dynamics simulation

Abstract

The floating body dynamics is treated as a Fluid-Structure Interaction (FSI) problem. A FSI problem is where the forces from the fluid move/deform the interacting structure, and the movement of the structure, in turn, influences the dynamics of fluid flow resulting in a coupled set of partial differential equations. The problem is especially challenging owing to the time changing nature of the domain and the presence of multiple interacting phases. These kind of time changing domain and multi physics problems are primarily dealt with moving domain or fixed grid techniques. In the moving domain technique, the governing equations are posed in the so called Arbitrary Lagrangian Eulerian (ALE) formulation. In ALE formulation, the interfaces are resolved by the mesh and thus leads to very good mass conservation properties. But the method fails when there are large topological changes, such as mixing and splitting. This problem can be partly handled by fixed grid techniques where a special function is used to represent various phases, but the method has its drawbacks, one of which is the interfaces cannot be represented precisely and smears with time which leads to mass conservation problems and often much finer mesh is needed to localize the interface. Also, because of the pure convection nature of the phase transport equation, a naive/standard discretization results in undershoots and overshoots of the solution. Special stabilization schemes have to be used to suppress the oscillations. The aim of the thesis is to treat the floating structure as a rigid body to estimate its overall stability in free surface flows.

First, the problem is posed in moving mesh or Arbitrary Lagrangian Eulerian framework. The motion of the free surface was captured. But the method failed to capture the dynamics of the floating structure when it is introduced. Fine tuning the mesh yielded only incremental result. So the research focus was shifted to fixed grid techniques, particularly the 'Volume of Fluid' (VoF) method. For the present problem, we took a hybrid approach. The interface between the floating structure and surrounding fluid/s is treated in a Lagrangian way, thus necessitating mesh movement, and the fluid-fluid interface (in our case, it can be considered as water-air) is captured by the VoF equation. As there is mesh movement, the VoF equation was also posed in ALE form.

As the VoF equation is a pure convection equation, a naive Galerkin discretization results in undershoots and overshoots in the solution. The Streamlined Upwind Petrov Galerkin (SUPG) stabilization is used to stabilize the VoF equation. The scheme is shown to give stable results. The Finite element method is used to discretize the coupled set of partial differential equations. The method is extensively discussed in a moving mesh setting with various boundary conditions. The partitioned time stepping is used to march in time across phases, and a fully implicit scheme is employed within each phase.

Finally, this hybrid ALE-NSE-VoF with SUPG stabilization scheme is shown to give stable results for extended time steps. The numerical results with both the formulations(ALE and VoF) are discussed. The simulations are carried out in distributed setting with Message passing interface(MPI), and the speedup results are discussed as well.