# Presentation: 515541

## The TeraScale Supernova Initiative (TSI)

***Shedding New Light on Exploding Stars:***
***TeraScale Simulations of Neutrino-Driven***
***Supernovae and Their Nucleosynthesis***** **

**Oak Ridge National Laboratory**
**SUNY at Stony Brook**
**University of Illinois at Urbana-Champaign**
**University of Tennessee Knoxville**
**University of California San Diego**
**North Carolina State University**
**University of Washington**
**Florida Atlantic University**
**Clemson University**

## Investigator Team

_***Nuclear Structure Computations***_
_***for EOS, Nucleosynthesis,  &***_
_*** ***__***Neutrino-Matter Interactions***_
**D. Dean (ORNL, U Tenn.)**
**G. Fuller (UC San Diego)**
**W. Haxton (U. Washington)**
**J. Lattimer (SUNY Stony Brook)**
**B. Meyer  (Clemson)**
**M. Prakash (SUNY Stony Brook)**
**M. Strayer (ORNL)**

_***Linear System  Algorithms***_
**J. Dongarra (U. Tenn.)**
**F. Saied (U. of Illinois)**
**P. Saylor (U. of Illinois)**

_***Visualization***_
**P. Baker (U. of Illinois)**
**R. Toedte (ORNL)**

_***Radiation Hydrodynamics &***_
_***Supernova Simulations***_
**J. Blondin (NC State)**
**S. Bruenn (Florida Atlantic U.)**
**J. Hayes (UC San Diego)**
**T. Mezzacappa (P.I.) **** (ORNL)**
**D. Swesty (SUNY Stony Brook)**

##  e- + p --> n +  e   (neutronization)

**For stars w/  M > 10 M****sol   ****the**
**iron core (M****Fe**** ~ 1.2-1.3 M****sol****) **
**collapses violently ****(core collapse)**

**Core bounce produces a strong shock**
**wave that weakens & stalls before reaching**
**edge of iron core ****(prompt phase)**

**Collapse halts when central densities**
**exceed  5x10****14**** g/cm****3  ****(core bounce)**

**Neutrinos move through matter via **
**radiative transport**** ****(neutrino transport)**

**Shock-heated matter produces neutrino/**
**anti-neutrino pairs  ****(pair production) ****in**
**3 flavors (electron, muon, tauon)**

**Electron type neutrinos are produced by**
** ****e****- ****+ p --****>**** n +  ********e****   ****(neutronization)**

## Shock radius 100-200 Km

**Shock radius 100-200 Km**

**Proto-neutron**
**star radius**
**15-50 Km**

## Neutrino reheating of material below

**stalled shock may contribute to driving**
**the convection**

**Negative entropy gradient drives**
**convection behind the stalled shock**

**Core collapse ****(Type II)**** supernovae **
**are thought to be driven by this **
**combination of convection  and **
**neutrino reheating**

**In contrast  ****Type I supernovae**** are**
**driven by thermonuclear chemistry**
**and are totally unrelated to core collapse**
**supernovae**

## Supernova Simulation Components

**Eulerian Hydrodynamics (explicit algorithms)**
**Newtonian hydrodynamics**
**General relativistic hydrodynamics**
**Neutrino transport (implicit algorithms)**
**Boltzmann transport**
**Sparse systems algorithms ****(matrix-free)**
**Preconditioners**
**Multi-group, Flux-limited Diffusion **
**Sparse systems algorithms**
**Preconditioners**
** ****Opacities**
** ****Neutrino absorption/emission rates**
** ****Equation of state (EOS) model**
** ****Reactive flow nuclear chemistry**

## Neutrino Transport

_***Neutrino Transport***_

***Boltzmann equation***

***Multi-group flux-limited diffusion ******(MGFLD)****** equation***

## Mathematical Challenges

**Iterative methods for discretized Boltzmann and MGFLD equations**
**Parallel preconditioners for discretized Boltzmann and MGFLD equations**
**Effective preconditioners for block-structured AMR**
**Methods for dealing with stiff coupling terms resulting from matter-radiation energy exchange**
**Methods for dealing with non-linearities in source terms**
**Can we solve both hydro and transport equations simultaneously?  Newton-Krylov?**

## Linear systems characteristics

***Non-symmetric***
***Block structured with outlying bands ***
***Center blocks are dense***
***1 set of outlying bands for problems  w/ 1 spatial dimension***
***2 sets of outlying bands for problems w/ 2 spatial dimensions***
***3 sets of outlying bands for problems w/ 3 spatial dimensions***
**Matrices are usually M-matrices for pure transport problems**
**Structure will be more complex w/ AMR**
**Memory requirements:****  initially ****25-50 Gbytes**** assuming matrix-free methods;   increasing to ****250 Gbytes**** in outyears**

## Typical 3-D sparsity pattern

***Typical 3-D sparsity pattern***

***Typical field of values ***
***&   Eigenvalues***

## Supernova Simulation Timeline

***Year 0***

***Year 1***

***Year 2***

***Year 3***

***Year 4***

***Year 5***

***3-D MGFLD Models ******(4D)***

***3-D MGFLD Models w/ AMR ******(4D)***

***2-D MGFLD Models ******(3D)***

***2-D Boltzmann Models ******(5D)***

***1-D Boltzmann Models ******(3D)***

***3-D Boltzmann Models ????? ******(7D)***

## Software Engineering Issues

***Our  codes  are written (or are being written) as ******F90+MPI****** codes***
*** ******TSI****** collaboration w/******  ******IBEAM ******Project***
***IBEAM =****** ******I******nteroperability ******B******ased****** ******E******nvironment****** ******for ******A******daptive ******M******eshes***
***IBEAM will be an ******F90 + MPI******  object oriented framework for astrophysical simulation.  It will be made ******publicly  available***
***AMR will be done with the ******PARAMESH ******package developed by ******NASA GSFC****** ESS HPCC Team***
***Current collaboration:   ******TSI ******+ ******ASCI Flash Center****** + ******NASA GSFC****** + ******other NASA funded researchers***
***How will this fit in with TOPS & CCA plans????***