Asymptotic Solutions and Numerical Methods for some Freeboundary Problems in Fluid MechanicsTools Fan, Yiyun (2023) Asymptotic Solutions and Numerical Methods for some Freeboundary Problems in Fluid Mechanics. PhD thesis, University of Nottingham.
AbstractFreeboundary 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 freeboundary problems in inviscid fluid mechanics using asymptotic and numerical methods. We construct new asymptotic solutions for the twofluid dambreak problem and a solid/twofluid interaction problem with an inclined accelerating plate, and develop the numerical methods based on the finite element method for generic freeboundary problems.
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