On the detection of a moving obstacle in an ideal fluid by a boundary measurement

Carlos Conca, Patricio Cumsille, Jaime Ortega, Lionel Rosier
2008 Inverse Problems  
Inverse problems in fluid mechanics constitute a challenging topic with numerous potential applications, ranging from engineering, medicine, and military surveillance to fishing. In this case we are interested in to study the existence and uniqueness of a model which describe the dynamic of a fluid-solid system, in particular the fluid considered is non viscous and the dynamic of the solid B(t) is due to its interaction with the fluid. Firstly we will discuss the existence and uniqueness of
more » ... tions of the model which describe this system when the fluids fulfills an unbounded region R 2 \ B(t). Later we will discuss the existence and uniqueness when the fluid fulfills a bounded region Ω(t) = Ω \ B(t). Finally, we study the problem of obtain some information about the solid through the observation of the velocity at some part Γ of the exterior boundary ∂Ω. To do this, firstly we analyze the well-posedness of the problem and we obtain the determination of the position and the velocity of the obstacle from a boundary measurement of the velocity of the fluid at a given time t. Some numerical results will be presented. ------------------
doi:10.1088/0266-5611/24/4/045001 fatcat:shaajl2hsjb5jcpvex2dnewc2m