Mathematical modeling of the interaction between two-phase environmental flow and protective hydraulic structures

In August 2005, Hurricane Katrina struck the Gulf Coast of the United States. Over a thousand people lost their lives and the total damage was about 108 billion USD. It was the costliest United States hurricane. Two-thirds of the deaths and majority of economical loss were related to the protection system failure. This drives the study of fluid structure interaction to properly design the levees and floodwalls in the future for flooding vulnerable areas. Fluid-structure interaction is the interaction between a deformable structure and the surrounding flow. The fluid causes the deformation of the solid, and the solid reacts to the fluid. This thesis will focus on the interactions between two-phase environmental flow (air and water), and hydraulic structures (e.g. floodwalls, etc.) which are partially submerged in the water to disrupt the flow. Hydrodynamic and hydrostatic forces and impact loads from high water levels and velocities applied to the interface must be carefully monitored, as well as their impact on the structural stability. The main purpose of this work is to give a deeper understanding to the interaction processes and the coupling effects, and to determine the possible deformation or critical values of overturning moments for more robust future designs of floodwalls and levees. There are two main approaches to simulate fluid-solid interactions: the monolithic approach and the partitioned approach. In this work we use the partitioned approach by looking into the separate flow and structure models and simulating the interaction process. For the two-phase flow subproblem, the interface of air and water is treated as a material discontinuity in modeling, and is tracked by the level set method. The coupled system consists of Navier-Stokes Equation, level set method and the volume of fraction method, solved by the splitting method with residual-based variational multi-scale methods for stabilization. The structural mechanics is modeled by linear elasticity. Different types of floodwalls and two factors of safety against sliding and overturning are studied. In the Galveston area, the soil and floodwall properties determine the necessity to include soil as a part of the model. Hyperelastic and plastic models are discussed in simulating the soil behavior. The interaction process is modeled by imposing the matching conditions on the common fluid-structure boundary. Both one-way and two-way interaction models under synthetic waves are discussed and compared. One-way interaction is saving in computation and used widely in engineering design. Two-way interaction is formulated under the Arbitrary Lagrangian-Eulerian(ALE) framework. The operator splitting technique is developed for the coupled system to reduce computing cost while remain high accuracy.