MSMoE40
Extreme Behavior in Flow Models: Analysis and Computations
Date: August 10
Time: 16:0018:30
Room: 303A
(Note: Click title to show the abstract.)
Organizer:
Protas, Bartosz (McMaster Univ.)
Takashi, Sakajo (Kyoto Univ.)
Abstract: The minisymposium has for its objective to explore from the
computational perspective extreme, and possibly singular, behavior in
various PDE models of fluid flows. Such questions are motivated by the
"blowup" problem for the 3D NavierStokes system which is one of open
problems in mathematics. In addition to the NavierStokes and Euler
systems, the symposium will cover other simplified model problems in
1D and 2D, as well as vortex models, focusing on the interplay between
mathematical analysis and careful numerical computations. Specific
topics to be discussed include analytical and numerical criteria for
blowup, choice of initial data and simulation strategies.
MSMoE401
16:0016:30
Extreme Vortex States and the Hydrodynamic BlowUp Problem
Protas, Bartosz (McMaster Univ.)
Abstract: We will discuss our research program concerning a systematic search
for extreme events in viscous incompressible flows. It is motivated
by questions related to singularity formation in the 3D NavierStokes
system and other hydrodynamic models. We will demonstrate how new
insights concerning extreme behavior in such models can be obtained by
formulating these questions in terms of variational PDE optimization
problems which can be solved computationally using discrete gradient
flows. [Joint work with Diego Ayala]
MSMoE402
16:3017:00
On the generalized nonviscous/viscous DeGregorio equation  singular solutions and statistical properties
Takashi, Sakajo (Kyoto Univ.)
Abstract: The generalized DeGregorio equation is a 1D model of the 3D Euler equations and NavierStokes equations. This equation is obtained by adding an advection term and the viscous dissipation term to the ConstantinLaxMajda equation. In this talk, I am concerned with the relation between singular blowup solutions to the for nonviscous equation as well as a "turbulent" statistical properties of solutions to the equation with small viscosity.
MSMoE403
17:0017:30
Assessing latetime singular behaviour in symmetryplane models of 3D Euler flow
Bustamante, Miguel (Univ. College Dublin)
Abstract: We introduce a oneparameter family of models of the 3DEuler fluid equations on a 2D symmetry plane, which provide a collection of blowup scenarios admitting analytical solutions. We exploit these features to validate a novel finitetime blowup assessment method in numerical simulations: the mapping to regular systems. We show a 3orderofmagnitude accuracy increase on the measured singularity time when employing the mapping, with negligible computational expense. Relevant blowup quantities include vortexstretching rate and analyticitystrip width.
MSMoE404
17:3018:00
Burgers vortex system and Hermite polynomials
Kimura, Yoshifumi (Graduate School of Mathematics, Nagoya Univ.)
Abstract: The Burgers vortex is wellknown as a steady exact solution of the NavierStokes equation which is often used as a model for vortex motion in turbulence. In this talk, we extend this solution first to a time dependent problem, and then to the motion of a group of gaussian vortices. It will be shown that the solution for the latter problem is written with the superposition of Hermite polynomials.
MSMoE405
18:0018:30
Computerassisted proofs in incompressible fluids
GomezSerrano, Javier (Princeton Univ.)
Abstract: In this talk I will discuss how, guided by numerical simulations, one can accomplish to produce completely rigorous, computerassisted theorems in problems related to fluid mechanics using interval arithmetics. Specifically, I will talk about the Muskat and the vortex patch (and its generalization known as the alphapatch) problems. The talk is based in joint work with Angel Castro, Diego Cordoba, Rafael GraneroBelinchon and Alberto Martin Zamora.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
