6 research outputs found
On the Stability of Thermonuclear Burning Fronts in Type Ia Supernovae
The propagation of cellularly stabilized thermonuclear flames is investigated
by means of numerical simulations. In Type Ia supernova explosions the
corresponding burning regime establishes at scales below the Gibson length. The
cellular flame stabilization - which is a result of an interplay between the
Landau-Darrieus instability and a nonlinear stabilization mechanism - is
studied for the case of propagation into quiescent fuel as well as interaction
with vortical fuel flows. Our simulations indicate that in thermonuclear
supernova explosions stable cellular flames develop around the Gibson scale and
that deflagration-to-detonation transition is unlikely to be triggered from
flame evolution effects here.Comment: 6 pages, 2 figures, to appear in the proceedings of the IAU
Colloquium 192, "Supernovae (10 years of SN1993J)", 22-26 April 2003,
Valencia, Spain, Eds. J.M. Marcaide and K.W. Weiler, Springer Verla
Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes
We consider an algorithm called FEMWARP for warping triangular and
tetrahedral finite element meshes that computes the warping using the finite
element method itself. The algorithm takes as input a two- or three-dimensional
domain defined by a boundary mesh (segments in one dimension or triangles in
two dimensions) that has a volume mesh (triangles in two dimensions or
tetrahedra in three dimensions) in its interior. It also takes as input a
prescribed movement of the boundary mesh. It computes as output updated
positions of the vertices of the volume mesh. The first step of the algorithm
is to determine from the initial mesh a set of local weights for each interior
vertex that describes each interior vertex in terms of the positions of its
neighbors. These weights are computed using a finite element stiffness matrix.
After a boundary transformation is applied, a linear system of equations based
upon the weights is solved to determine the final positions of the interior
vertices. The FEMWARP algorithm has been considered in the previous literature
(e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing
deformed meshes for certain applications. However, sometimes FEMWARP reverses
elements; this is our main concern in this paper. We analyze the causes for
this undesirable behavior and propose several techniques to make the method
more robust against reversals. The most successful of the proposed methods
includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in
BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7
September 2010. Published online on 9 October 2010. The final publication is
available at http://www.springerlink.co