CASPER Seminar - Adaptive Splitting Methods in Application to a Solid Fuel Ignition Model
Dr. Matthew Beauregard, Department of Mathematics, Center of Atmospheric, Space and Engineering Research, Baylor University
|Date||January 25, 2013||Time||1:30 - 2:30 pm|
|Description||Various types of partial differential equations have been playing increasingly
important roles in the study of theoretical and numerical combustion.
The heat distribution of a premixed, solid-fuel combustor can
be decoupled from the activation energy leading to a singular, nonlinear,
and degenerate reaction-diffusion equation. A Peaceman-Rachford
splitting based adaptive method is developed. Spatial adaptation is accomplished
through modified equidistribution principles that stem from
a priori solution information. This generates non-uniform exponentially
evolving grids. Rigorous numerical analysis are given to ensure the satisfactory
effectiveness, efficiency, and numerical stability of the developed
scheme. Simulation experiments are provided to illustrate these accomplishments.
A brief history is provided, while many open problems are
illustrated throughout the discussion.
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