Title: Flame modeling and Rayleigh-Taylor instabilities in Type Ia
Supernovae

Abstract

Supernova explosions are spectacular events, playing important role in
astrophysics and cosmology.  Supernovae are responsible for the fusion of
heavy elements in the Universe;  their light curves allow us to measure the
distances to the host galaxy and quantify the expansion of the Universe.
The explosion of type Ia supernova starts with deflagration (flame) when a
bubble of  hot and light reaction products rises from interior of the star
to its surface, while reaction continues on the surface of the bubble.  The
top surface of the bubble is subject to Rayleigh-Taylor instability -  an
instability of an interface between heavy fluid above and light fluid
below, - which wrinkles the flame and enhances overall reaction rate.

Numerical simulation of type Ia supernova are facing several challenges,
one of them is that the width of the nuclear flame is unresolvable on the
scale of the star.   Typically this kind of problems are addressed by
implementing front tracking or front capturing models.  In multi-physics
problems, a special attention must be paid to ensure that such model is
integrated with the rest of the physics.  In my talk, I present the
development of the flame-capturing model based on
 advectionâ??reactionâ??diffusion equation implemented in FLASH code, a
parallel high-performance community code for astrophysical simulation.

The other challenge is understanding the effect of Rayleigh-Taylor
instability on flame propagation.  I study a model version of this
phenomenon -  the limit of small density differences (Boussinesq
approximation).  Even though the model accounts for only essential physics
- gravity, reaction, and diffusion, - the numerical simulations are
non-trivial task because of the rapidly increasing range of spatial scales.