Annual Report 2008.pdf - SAMSI

University of California, Irvine
Department of Mathematics
gpatrick@math.uci.edu
“A Free Boundary Problem with Phase Onset”
A class of diffusive Free Boundary Problems will be introduced which is characterized by the
initial instantaneous onset of a phase. It leads to the study of singular (initial) boundary value
problems. The techniques that needed to be developed in order to treat its well-posedness will be
presented along with their application to a practically relevant model of case II diffusion.
Guowei He
Iowa State University
Department of Aerospace Engineering
guoweihe@yahoo.com
“A Hybrid Approach of Large-Eddy Simulation and Immersed Boundary for Flapping Wings at
Moderate Reynolds Numbers”
Numerical simulation of flapping wings at moderately high Reynolds numbers presents two
challenges to computational fluid dynamics: turbulent flows and moving boundaries. On the one
hand, direct numerical simulation of turbulent flows is not feasible in practice due to current
capability of computer and the Reynolds averaging Navier-Stokes method is difficult in
predicting the unsteady properties of turbulent flows. Instead, large-eddy simulation, which
simulates 调 和 the motions of large-scale eddies with modeling the effects of small-scale eddies
on large-scale ones, becomes a powerful simulation technique for turbulent flows; On the other
hand, moving boundaries usually need body-fitting girds and the grid generation is timeconsuming.
Immersed boundary method uses non-body-fitting grids which can treat the moving
boundaries on Cartesian grids efficiently. Therefore, a combination of large-eddy simulation and
immersed boundary method is promising that can efficiently simulate the unsteady aerodynamics
of flapping wings. In this talk, I will introduce our recent work on how to combine large-eddy
simulation and the immersed boundary method. The hybrid approach is used to simulate a
SD7003 airfoil in plunge and/or pitch motions at Re=60,000. The results obtained are compared
with the previous numerical simulations and experimental measurements.
Shi Jin
University of Wisconsin-Madison
Department of Mathematics
jin@math.wisc.edu
“Numerical Computation of High Frequency Waves through Interfaces”
We introduce Eulerian methods that are efficient in computing high frequency waves through
interfaces. The method is based on the classical Liouville equation in phase space, with
discontinous Hamiltonians (or singular coefficients) due to the barriers or material interfaces.
We provide physically relavant interface conditions consistent with the correct transmissions and