# Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution

## Abstract

The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Advanced ScientificComputing Research

- OSTI Identifier:
- 920061

- Report Number(s):
- LBNL-58673-Pt.II

Journal ID: ISSN 0004-637X; ASJOAB; R&D Project: K11001; BnR: KJ0101010; TRN: US200822%%707

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 649; Journal Issue: 2pt1; Related Information: Journal Publication Date: 10/02/2006

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS; ALGORITHMS; EXPLOSIONS; HEAT SOURCES; HYDRODYNAMICS; IGNITION; MACH NUMBER; SIMULATION; STELLAR ATMOSPHERES; SUPERNOVAE; VALIDATION; supernovae: general white dwarfs hydrodynamics convectionmethods:numerical

### Citation Formats

```
Almgren, Ann S., Bell, John B., Rendleman, Charles A., and Zingale,Mike.
```*Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution*. United States: N. p., 2006.
Web.

```
Almgren, Ann S., Bell, John B., Rendleman, Charles A., & Zingale,Mike.
```*Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution*. United States.

```
Almgren, Ann S., Bell, John B., Rendleman, Charles A., and Zingale,Mike. Tue .
"Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution". United States.
doi:. https://www.osti.gov/servlets/purl/920061.
```

```
@article{osti_920061,
```

title = {Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution},

author = {Almgren, Ann S. and Bell, John B. and Rendleman, Charles A. and Zingale,Mike},

abstractNote = {The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.},

doi = {},

journal = {Astrophysical Journal},

number = 2pt1,

volume = 649,

place = {United States},

year = {Tue Mar 28 00:00:00 EST 2006},

month = {Tue Mar 28 00:00:00 EST 2006}

}