Asymptotic Solutions and Numerical Methods for some Free-boundary Problems in Fluid Mechanics - Fan, Yiyun (2023)
Free-boundary problems are encountered in a wide range of applications in fluid mechanics, such as the interaction of a ship with the surface of the ocean, and the failure of a dam. Since the free boundary is unknown and part of the solution, such problems are nonlinear and rarely have analytical solutions. In this thesis, we formulate and solve some free-boundary problems in inviscid fluid mechanics using asymptotic and numerical methods. We construct new asymptotic solutions for the two-fluid dam-break problem and a solid/two-fluid interaction problem with an inclined accelerating plate, and develop the numerical methods based on the finite element method for generic free-boundary problems.