On the applicability of the level set method beyond the flamelet regime in thermonuclear supernova simulations

Abstract

In thermonuclear supernovae, intermediate mass elements are mostly produced by distributed burning provided that a deflagration to detonation transition does not set in. Apart from the two-dimensional study by Röpke & Hillebrandt (2005, A&A, 429, L29), very little attention has been payed so far to the correct treatment of this burning regime in numerical simulations. In this article, the physics of distributed burning is reviewed from the literature on terrestrial combustion and differences which arise from the very small Prandtl numbers encountered in degenerate matter are pointed out. Then it is shown that the level set method continues to be applicable beyond the flamelet regime as long as the width of the flame brush does not become smaller than the numerical cutoff length. Implementing this constraint with a simple parameterisation of the effect of turbulence onto the energy generation rate, the production of intermediate mass elements increases substantially compared to previous simulations, in which the burning process was stopped once the mass density dropped below 10 7 g cm −3 . Although these results depend on the chosen numerical resolution, an improvement of the constraints on the the total mass of burning products in the pure deflagration scenario can be achieved.

TURBULENCE IN A THREE-DIMENSIONAL DEFLAGRATION MODEL FOR TYPE Ia SUPERNOVAE. II. INTERMITTENCY AND THE DEFLAGRATION-TO-DETONATION TRANSITION PROBABILITY

“…Apart from this, the propagation of the burning zone has to be treated beyond the onset of distributed burning. Schmidt (2007) proposed that the level set technique can be extended at least into the broken-reaction-zones regime (Kim & Menon 2000), provided that the burning time scale does not exceed some fraction of the eddy turn-over time corresponding to the numerically unresolved velocity fluctuations (i. e., the ratio of the grid cell size to the square root of the specific subgrid scale turbulence energy). This approach also calls for further microphysical studies.…”

A Three‐Dimensional Deflagration Model for Type Ia Supernovae Compared with Observations

“…The threshold for burning to intermediatemass elements was chosen lower than in previous simulations. As argued by Schmidt (2007) the level-set description of the flame propagation may be extended beyond the onset of distributed burning at which turbulent eddies penetrate the internal structure (the ''thin reaction zones regime''). This commences as soon as the flame width becomes larger than the Gibson scale, an effect that is expected to occur at fuel densities $10 7 g cm À3 .…”

“…Here, the problem of modeling the flame propagation at conditions where the flamelet picture breaks down becomes important. It has been shown that a flame acceleration in this phase would significantly enhance the production of intermediate-mass elements and the energy release ( Röpke & Hillebrandt 2005b), but Schmidt (2007) argues that such an acceleration does not occur and that a continuation of modeling the flame propagation as in the flamelet regime is possible. This approach was followed here, too.…”

Thermonuclear Supernovae

“…Then, turbulence penetrates the internal structure of the flame and it enters the regime of distributed burning [73]. Including this burning stage into thermonuclear supernova simulations [46,76] affects the latest stages of deflagration burning.…”