Annual Report 2008.pdf - SAMSI

waw@case.edu
“Classical and Fractional Models in Nonlinear Porous Media”
The talk will present an overview of the classical nonlinear porous medium equation as well as
the more recent efforts at developing nonlinear fractional models that would permit non-classical
scaling behavior, different from Barenblatt asymptotics. Mathematical underpinnings as well as
computational Monte Carlo-style methods via interacting particle systems will be discussed.
Jack Xin
University of California-Irvine
Department of Mathematics
zhanglucy@rpi.edu
“Reaction-Diffusion Fronts in Random Flows”
In this expository talk, we shall review the analysis of front solutions of stochastic reactiondiffusion-advection
equations using large deviation and maximum principle approaches. We
begin with a background of such problems arising in turbulent combustion and basic
probabilistic tools, and end with open problems on fronts (interfaces) in random media.
Lucy Zhang
Rensselaer Polytechnic Institute
Department of Mechanical, Aerospace, and Nuclear Engineering
zhanglucy@rpi.edu
“Fluid and Deformable-Structure Interactions in Bio-Mechanical Systems”
Fluid-structure interactions exist in many aspects of our daily lives. Typical biomedical
engineering examples are blood flowing through a blood vessel and in the heart. Recently, more
attentions are paid to the development of micro-air vehicles that require the designs of morphing
wings or flapping wings. Fluid interacting with moving or embedded structures poses more
numerical challenges for its complexity in dealing with transient and simultaneous interactions
between the fluid and solid domains. To obtain stable, effective, and accurate solutions is not
trivial. Traditional methods that are available in commercial software often generate numerical
instabilities.
In this talk, a novel numerical solution technique, Immersed Finite Element Method (IFEM), is
introduced for solving complex fluid-structure interaction problems in various engineering fields.
The fluid and solid domains are fully coupled, thus yield accurate and stable solutions. The
variables in the two domains are interpolated via a delta function induced from one of the shape
functions used in meshfree methods. This approach enables the use of non-uniform grids in the
fluid domain, which allows the use of arbitrary geometry shapes and boundary conditions. This
method extends the capabilities and flexibilities in solving various biomedical, traditional
mechanical, aerospace, and nuclear engineering problems with detailed and realistic mechanics
analysis. Verification problems will be shown to validate the accuracy and effectiveness of this