# A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS

## Abstract

It is now generally agreed that multidimensional, multigroup, neutrino-radiation hydrodynamics (RHD) is an indispensable element of any realistic model of stellar-core collapse, core-collapse supernovae, and proto-neutron star instabilities. We have developed a new, two-dimensional, multigroup algorithm that can model neutrino-RHD flows in core-collapse supernovae. Our algorithm uses an approach similar to the ZEUS family of algorithms, originally developed by Stone and Norman. However, this completely new implementation extends that previous work in three significant ways: first, we incorporate multispecies, multigroup RHD in a flux-limited-diffusion approximation. Our approach is capable of modeling pair-coupled neutrino-RHD, and includes effects of Pauli blocking in the collision integrals. Blocking gives rise to nonlinearities in the discretized radiation-transport equations, which we evolve implicitly in time. We employ parallelized Newton-Krylov methods to obtain a solution of these nonlinear, implicit equations. Our second major extension to the ZEUS algorithm is the inclusion of an electron conservation equation that describes the evolution of electron-number density in the hydrodynamic flow. This permits calculating deleptonization of a stellar core. Our third extension modifies the hydrodynamics algorithm to accommodate realistic, complex equations of state, including those having nonconvex behavior. In this paper, we present a description of our complete algorithm, giving sufficientmore »

- Authors:

- Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, NY 11794-3800 (United States), E-mail: dswesty@mail.astro.sunysb.edu, E-mail: emyra@umich.edu

- Publication Date:

- OSTI Identifier:
- 21269288

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal, Supplement Series

- Additional Journal Information:
- Journal Volume: 181; Journal Issue: 1; Other Information: DOI: 10.1088/0067-0049/181/1/1; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0067-0049

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; APPROXIMATIONS; COLLISION INTEGRALS; COMPUTER ARCHITECTURE; ELECTRONS; EQUATIONS OF STATE; GRAVITATIONAL RADIATION; HERA STORAGE RING; HYDRODYNAMICS; MATHEMATICAL SOLUTIONS; MULTIPARTICLE SPECTROMETERS; NEUTRINOS; NEUTRON STARS; NONLINEAR PROBLEMS; PARTICLE IDENTIFICATION; RADIANT HEAT TRANSFER; RADIATION TRANSPORT; SIMULATION; TWO-DIMENSIONAL CALCULATIONS; VERIFICATION

### Citation Formats

```
Swesty, F. Douglas, and Myra, Eric S..
```*A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS*. United States: N. p., 2009.
Web. doi:10.1088/0067-0049/181/1/1; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Swesty, F. Douglas, & Myra, Eric S..
```*A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS*. United States. doi:10.1088/0067-0049/181/1/1; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Swesty, F. Douglas, and Myra, Eric S.. Sun .
"A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS". United States. doi:10.1088/0067-0049/181/1/1; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21269288,
```

title = {A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS},

author = {Swesty, F. Douglas and Myra, Eric S.},

abstractNote = {It is now generally agreed that multidimensional, multigroup, neutrino-radiation hydrodynamics (RHD) is an indispensable element of any realistic model of stellar-core collapse, core-collapse supernovae, and proto-neutron star instabilities. We have developed a new, two-dimensional, multigroup algorithm that can model neutrino-RHD flows in core-collapse supernovae. Our algorithm uses an approach similar to the ZEUS family of algorithms, originally developed by Stone and Norman. However, this completely new implementation extends that previous work in three significant ways: first, we incorporate multispecies, multigroup RHD in a flux-limited-diffusion approximation. Our approach is capable of modeling pair-coupled neutrino-RHD, and includes effects of Pauli blocking in the collision integrals. Blocking gives rise to nonlinearities in the discretized radiation-transport equations, which we evolve implicitly in time. We employ parallelized Newton-Krylov methods to obtain a solution of these nonlinear, implicit equations. Our second major extension to the ZEUS algorithm is the inclusion of an electron conservation equation that describes the evolution of electron-number density in the hydrodynamic flow. This permits calculating deleptonization of a stellar core. Our third extension modifies the hydrodynamics algorithm to accommodate realistic, complex equations of state, including those having nonconvex behavior. In this paper, we present a description of our complete algorithm, giving sufficient details to allow others to implement, reproduce, and extend our work. Finite-differencing details are presented in appendices. We also discuss implementation of this algorithm on state-of-the-art, parallel-computing architectures. Finally, we present results of verification tests that demonstrate the numerical accuracy of this algorithm on diverse hydrodynamic, gravitational, radiation-transport, and RHD sample problems. We believe our methods to be of general use in a variety of model settings where radiation transport or RHD is important. Extension of this work to three spatial dimensions is straightforward.},

doi = {10.1088/0067-0049/181/1/1; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Astrophysical Journal, Supplement Series},

issn = {0067-0049},

number = 1,

volume = 181,

place = {United States},

year = {2009},

month = {3}

}