### Abstract

A new computationally efficient method has been introduced to treat self-gravity in Eulerian hydrodynamical simulations. It is applied simply by modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method cannot only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids, and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.

Original language | English |
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Article number | 083006 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 93 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2016 Apr 12 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*93*(8), [083006]. https://doi.org/10.1103/PhysRevD.93.083006

**Hyperbolic self-gravity solver for large scale hydrodynamical simulations.** / Hirai, Ryosuke; Nagakura, Hiroki; Okawa, Hirotada; Fujisawa, Kotaro.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 93, no. 8, 083006. https://doi.org/10.1103/PhysRevD.93.083006

}

TY - JOUR

T1 - Hyperbolic self-gravity solver for large scale hydrodynamical simulations

AU - Hirai, Ryosuke

AU - Nagakura, Hiroki

AU - Okawa, Hirotada

AU - Fujisawa, Kotaro

PY - 2016/4/12

Y1 - 2016/4/12

N2 - A new computationally efficient method has been introduced to treat self-gravity in Eulerian hydrodynamical simulations. It is applied simply by modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method cannot only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids, and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.

AB - A new computationally efficient method has been introduced to treat self-gravity in Eulerian hydrodynamical simulations. It is applied simply by modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method cannot only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids, and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.

UR - http://www.scopus.com/inward/record.url?scp=84963648016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963648016&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.93.083006

DO - 10.1103/PhysRevD.93.083006

M3 - Article

VL - 93

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

M1 - 083006

ER -