Application Of The Fictitious Domain Method On Wave-Structure Interaction

Water wave is an important hydrodynamic factor in offshore and coastal engineering. It is an engineering problem with many practical aspects such as the swash of seabed, the stagnation of contamination, the settlement of sand around the coastal structures, and the resonance of structures. So, wave-structure interaction is a very important problem in design, construction and management of offshore and coastal engineering.Wave-structure interaction consists two processes, i.e., the deformation and displacement of structures under the wave force and the change of wave shape and wave force due to the structures'deformation and displacement. These two processes are simultaneous and interactive. In the early studies, limited by the computational techniques, researchers used to either take the fixed-structure hypothesis and focus on the transformation of wave, the distribution of unknowns and the wave force on structures, or assume the wave force follows a given function and emphasis on the deformation and displacement of structures. Accompany with the improvement in computer science recently, researchers began to study on the interaction process of wave and structures by solving the wave field and structure field alternately. The solving processes are separated into two isolated domains, i.e., the fluid domain and structure domain, and coupled by fluid-structure interfaces. For the alternation feature of this method, it is not a fully coupled wave-structure interaction.Borrowing the ideas from the Fictitious Domain (FD) method in the multi-phase flows area, a set of fluid-solid fully coupled governing equations on wave-structure interaction is presented. In this method, the structures are taken as'fictitious'fluid with zero strain rate and the whole computational domain (includes fluid and solid) is governed by the Navier-Stokes equations. To keep the rigid body shape of the'fictitious'fluid, the Distributed Lagrangian Multiplier (DLM) method is applied on the'fictitious'domain. In this set of coupled equations, the whole field is described by velocity and pressure, which are updated synchronously. So, in this manner, the solving process is a fully coupled wave-structure interaction.In the solving process of Navier-Stokes equations, the Characteristic method is adopted to handle the numerical oscillations in the high Reynolds convection dominated flows. The residual generalized Stokes problem can be easily solved by theUzawa/conjugated gradient method. Numerical results on 2-D cavity flow and 2-D cylinder flow provide convincing evidences for the method's excellent solution quality and fidelity.To simulate the free-surface flows, a novel VOF-type volume-tracking method based on unstructured triangular mesh is presented. In this method, the Piecewise Linear Interface Calculation (PLIC) method is adopted to obtain a second-order reconstructed interface approximation and the Modified Lagrangian-Eulerian Re-map (MLER) method is applied to accomplish the interface convection. Since the inherent merit of unstructured triangular mesh in fitting curved boundaries, this method can handle the free-surface problems with complex geometries accurately and directly, without introducing any complicated boundary treatment or artificial diffusion. To validate this method, a series of interface reconstruction and convection tests were performed to establish the high accuracy and second-order convergence rate of the solutions.Combining the Navier-Stokes equation solver and the VOF method based on unstructured triangular mesh, a vertical 2-D numerical wave tank is presented. In this numerical wave tank, an absorbable numerical wave maker is settled on the left boundary to generate the incident wave and a sponge layer is placed before the right boundary to absorb the wave energy. Small amplitude wave simulation results state the high accuracy of the solutions.Applying the vertical 2-D numerical wave tank, together with the structure's mechanical model, a numerical wave tank considering wave-structure interaction is established. By using this numerical wave tank, the interaction process between wave and structures with different size is simulated.