Thinking Outside the Box: Numerical Relativity with Particles
Abstract
:1. Introduction
2. SPHINCS_BSSN
2.1. Hydrodynamic Evolution
2.1.1. Dissipative Terms
2.1.2. Slope-Limited Reconstruction in the Dissipative Terms
2.1.3. Steering the Dissipation Parameter
2.2. Spacetime Evolution
2.3. Coupling between Fluid and Spacetime
2.4. Equations of State
- SLy [48]: with a maximum TOV mass , tidal deformability of a 1.4 star
- APR3 [49]: ,
- MPA1 [50]: ,
- MS1b [51]: , .
2.5. Constructing Initial Data for Binary Neutron Stars
2.6. Summary of the New Elements
- We enhance the slope limiter used in the reconstruction (minmod) by an exponential suppression term that enhances the dissipation for those rare cases where particles should get too close to each other; see Section 2.1.2. The effect of this change is only tiny, but we mention it for completeness.
- We trigger dissipation based on a shock indicator similar to [28] and a noise indicator suggested for the SPHINCS_SR code [29]; see Section 2.1.3.
- As in our previous study [16], we use a MOOD approach to decide which kernel to use in the mapping, but here, we use a more sophisticated acceptance measure; see our Section 2.3.
- We use, for the first time in SPHINCS_BSSN, piecewise polytropic approximations to nuclear equations of state. These fits to cold nuclear matter equations of state are enhanced by thermal pressure contributions; see Appendix A for a detailed description.
3. Results
3.1. Shock Tube
3.2. Binary Mergers
3.2.1. Performed Simulations
3.2.2. Dynamical Evolution
3.2.3. Impact of the Thermal Index
3.2.4. The Triggering of Artificial Dissipation
3.2.5. Gravitational Wave Emission
3.2.6. Ejecta
4. Summary
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ADM | Arnowitt–Deser–Misner |
BH | Black Hole |
BSSN | formulation according to Baumgarte, Shapiro, Shibata, and Nakamura |
EOS | Equation Of State |
GR | General Relativity |
GW | Gravitational Wave |
SPH | Smooth Particle Hydrodynamics |
SPHINCS | Smooth Particle Hydrodynamics in Curved Spacetime |
Appendix A. Recovery Procedure for Piecewise Polytropic Equations of State
Appendix B. Which Resolution?
- TS1: the outer boundary in each coordinate direction is located at 375 (≈554 km), five refinement levels and grid points which corresponds to the finest grid resolution length of m. We use here our default, i.e., 6th order, Finite Differencing (“FD6”).
- TS2: same as TS1, but FD4
- TS3: same as TS1, but FD8
- TS4: same as TS1, but grid points, i.e., m
- TS5: same as TS1, but grid points, i.e., m.
- TS6: same as TS1, but grid points, i.e., m.
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Name | EOS | #Particles | [m] | [m] | Comment |
---|---|---|---|---|---|
MPA1_1mio | MPA1 | 499 | 188 | ||
MPA1_2mio | MPA1 | 369 | 172 | ||
MPA1_5mio | MPA1 | 244 | 117 | ||
MPA1_2mio_ | MPA1 | 369 | 161 | ||
MPA1_2mio_ | MPA1 | 369 | 149 | ||
APR3_1mio | APR3 | 499 | 145 | ||
APR3_2mio | APR3 | 369 | 136 | ||
APR3_5mio | APR3 | 244 | 106 | ||
SLy_1mio | SLy | 499 | 140 | ||
SLy_2mio | SLy | 369 | 106 | ||
MS1b_1mio | MS1b | 499 | 270 | ||
MS1b_2mio | MS1b | 369 | 222 |
Name | [ ] | [] | [] | [] | |
---|---|---|---|---|---|
MPA1_1mio | 3.6 | 0.23 | |||
MPA1_2mio | 1.6 | 0.21 | 0 | ||
MPA1_5mio | 1.2 | 0.24 | |||
MPA1_2mio_ | 2.8 | 0.16 | 0 | ||
MPA1_2mio_ | 1.8 | 0.22 | |||
APR3_1mio | 9.7 | 0.27 | |||
APR3_2mio | 2.1 | 0.22 | |||
APR3_5mio | 1.9 | 0.21 | |||
SLy_1mio | 0.21 | ||||
SLy_2mio | 0.18 | ||||
MS1b_1mio | 2.9 | 0.16 | 0 | ||
MS1b_2mio | 2.7 | 0.18 |
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Rosswog, S.; Diener, P.; Torsello, F. Thinking Outside the Box: Numerical Relativity with Particles. Symmetry 2022, 14, 1280. https://doi.org/10.3390/sym14061280
Rosswog S, Diener P, Torsello F. Thinking Outside the Box: Numerical Relativity with Particles. Symmetry. 2022; 14(6):1280. https://doi.org/10.3390/sym14061280
Chicago/Turabian StyleRosswog, Stephan, Peter Diener, and Francesco Torsello. 2022. "Thinking Outside the Box: Numerical Relativity with Particles" Symmetry 14, no. 6: 1280. https://doi.org/10.3390/sym14061280
APA StyleRosswog, S., Diener, P., & Torsello, F. (2022). Thinking Outside the Box: Numerical Relativity with Particles. Symmetry, 14(6), 1280. https://doi.org/10.3390/sym14061280