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Resolving the small length-scale of thermonuclear detonation waves (TNDWs) insupernovae is currently not possible in multidimensional full-star simulations.Additionally, multidimensional simulations usually use small, oversimplisticreaction networks and adopt an ad hoc transition criterion to nuclearstatistical equilibrium (NSE). The errors due to the applied approximations arenot well understood. We present here a new accurate and efficient numericalscheme that accelerates the calculations by orders of magnitudes and allows thestructure of TNDWs to be resolved. The numerical scheme has two importantingredients: (1) a burning limiter that broadens the width of the TNDW whileaccurately preserving its internal structure, and (2) an adaptive separation ofisotopes into groups that are in nuclear statistical quasi-equilibrium, whichresolves the time-consuming burning calculation of reactions that are nearlybalanced out. Burning is calculated in situ employing the required largenetworks without the use of post-processing or pre-describing the conditionsbehind the TNDW. In particular, the approach to and deviation from NSE arecalculated self-consistently. The scheme can be easily implemented inmultidimensional codes. We test our scheme against accurate solutions of thestructure of TNDWs and against homogeneous expansion from NSE. We show thatwith resolutions that are typical for multidimensional full-star simulations,we reproduce the accurate thermodynamic trajectory (density, temperature, etc.)to an accuracy that is better than a percent for the resolved scales (where theburning limiter is not applied), while keeping the error for unresolved scales(broadened by the burning limiter) within a few percent.

monthly notices of the royal astronomical society

An accurate and efficient numerical calculation of detonation waves in  multidimensional supernova simulations using a burning limiter and adaptive  quasi-statistical equilibrium