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Fluid Dynamics Seminar

Monday, April 20, 2009, 4:00 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

Two Problems in Interfacial Fluid Dynamics

David Ambrose

Department of Mathematics, Drexel University

Abstract

Much progress has been made in recent years for analysis and computing of free-surface problems in fluid dynamics, especially for solving initial value problems with smooth initial data. In this talk, we will discuss two problems which have received less attention so far. First, we will address the problem of computing time-periodic free- surface flows. In joint work with Jon Wilkening, the speaker has developed a numerical method for computing time-periodic solutions of nonlinear PDEs. As an application of this method, time-periodic solutions of the Benjamin-Ono equation are computed. Second, we will address the problem of continuing solutions past interface collisions, in the presence of surface tension. For this problem, we will introduce introduce a new formulation, finding a transport equation coupled to the Navier-Stokes or Euler equations. This transport equation describes not just how the location of the free surface moves, but also how the tangent directions to the free surface move. This is joint work with Helena Nussenzveig Lopes, Milton Lopes Filho, and Walter Strauss.