TITLE:

RECENT ADVANCES IN 2-DIMENSIONAL SIMULATIONS OF THE PATTERN-FORMING KURAMOTO-SIVASHINSKY EQUATION (No. 124)

DATE:

Friday, October 20th, 2006

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Peter Blomgren, Department of Mathematics, San Diego State University

ABSTRACT:

We present an overview of recent advances in numerical simulations of the two-dimensional Kuramoto-Sivashinsky equation, describing the flame-front deformation in a combustion experiment.
Algorithmic development includes a second order unconditionally A-stable scheme, using distributed approximating functionals (DAFs) for well-tempered, representation of the physical quantity and its derivatives. The simulator reproduces a multitude of patterns observed in experiments-in-the wild, including rotating 2-cell, 3-cell, hopping 3-cell, stationary 2, 3, 4, 5-cell, stationary 5/1, 6/1, 7/1, 8/2 two-ring patterns, etc. The numerical observation of hopping flame patterns — characterized by nonuniform rotations of a ring of cells, in which individual cells make abrupt changes in their angular positions while they rotate around the ring — is the first outside of physical experiments.
We show modal decomposition analysis of the simulated patterns, via the singular value decomposition (SVD), which exposes the spatio-temporal behavior in which the overall temporal dynamics is similar to that of equivalent experimental states. Symmetry-based arguments are used to derive normal form equations for the temporal behavior, and a bifurcation analysis of the associated normal form equations quantifies the complexity of patterns.
In addition we also discuss the effects on the pattern formation due to “other physics” in the system, including noise, which increases the propensity of dynamic cellular states, which seems to explain the generic behavior of related laboratory experiments; and thermalback-conduction.

HOST:

Jose Castillo

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