Department of Mathematics

The Florida State University

This Week in Mathematics

Special Edition

14 - 18 December 1998 1998

Monday: 14 December 1998

 

Special Colloquium, 10:00 a.m. in the SCRI seminar room, 499 SCL

       Jan S. Hesthaven, Division of Applied Mathematics, Brown University

          Absorbing Boundary Conditions for Acoustics

   When solving wave-dominated problems in domains of infinite extend one faces the issue of how to properly truncate the computational domain in a way such that the finite size computation correctly models the infinite domain problem. Although this question has recieved very considerable attention in the past it remains one of the central, yet essentially open, issues in the accurate modeling of such problems as they appear in e.g. electromagnetics, gas-dynamics, aero-acoustics and non-linear optics. In particular in connection with high-order methods must one address this problem carefully in order not to ruin the accurate interior solution by artificial reflections from the computational boundary.

   The 1994 introduction of the Perfectly Matched Layer (PML) methods, consisting of a spongelayer capable of absorbing all incoming waves, regardless of their frequency and angel of incidence, seemed at first to effectively eliminate this critical concern for problems of electromagnetics. However, subsequent analysis of the scheme has exposed many problems and much work is still needed along these lines.

   In this talk we shall focus the attention on the construction and analysis of PML methods for problems in acoustics. We shall begin by showing that the original approach by which the PML equations are obtained, utilizing a non-physical splitting of the equations, leads to loss of strong wellposedness. Following that, we first discuss PML schemes for the special case of ambient acoustics before addressing the more general, and much more complex, question of PML schemes for general convective aero-acoustics. Rather than using physical arguments, we shall present a very general mathematical procedure that allows us to derive a strongly wellposed PML scheme for the case of a constant mean flow. Computational experiments show its superior performance but also exposes a very curious problem with this, and all other PML methods, when subjected to a spatially low-frequency exitation. We shall conclude by explaining and resolving this issue.

 

Tuesday: 15 December

 

Wednesday: 16 December

 

Thursday: 17 December

 

Special Colloquium, 10:00 a.m. in the SCRI seminar room, 499 SCL

       Z. Jane Wang, Courant Institute of Mathematical Sciences, New York University

          Unsteady Aerodynamics of Insect Flight

   The myth "bumble-bees cannot fly according to convential aerodynamics" simply relects our poor understanding of unsteady viscous fluid dynamics. In particular, we lack a theory of vortex shedding at the intermediate Reynolds numbers relevant to insect flight. Laboratory measurements of time-dependent forces and vorticity in unsteady flows are still dificult. Understanding aerodynamics of insect flight is not only of theoretical interest, but is directly related to the current challenge of building micro-aviation vehicles.

   The Reynolds numbers of insect flight lie in the range of 100 to 10,000, which implies that both inertial and viscous effects are important. Moreover, wings flap rapidly, with frequencies in the range of 20 to 200 Hz, and produce highly unsteady flows. As a consequence, simple extensions of conventional aerodynamics using quasi-steady and inviscid approaches, have not been generally successful. Fortunately, with the recent advances in CFD, it is now feasible to compute the full flow around a moving wing at relevant Reynolds numbers. Such simulations can complement the existing laboratory experiments by quantifying both the vorticity and the forces, and can facilitate our search of optimal solutions. These computations can further suggest simple models for generating the observed aerodynamic forces.

 

Friday: 18 December

 

Seminars and colloquia at "that other" university [a.k.a. the University of Florida]

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