Equation of State in Numerical Relativistic Hydrodynamics

Ryu, Dongsu; Chattopadhyay, Indranil; Choi, Eunjin

doi:10.1086/505937

Cited by 100 publications

(172 citation statements)

References 24 publications

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“…Under the condition (39), W i,j,k (0) ∈ G * implies ǫ > 0, and that W i,j,k (0) belongs to G ǫ defined in (29). We then have the following property, whose proof is displayed in Appendix A 6.…”

Section: Pcp Flux Limitermentioning

confidence: 95%

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

2017

Phys. Rev. D

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The paper develops high-order physical-constraint-preserving (PCP) methods for general relativistic hydrodynamic (GRHD) equations, equipped with a general equation of state. Here the physical constraints, describing the admissible states of GRHD, are referred to the subluminal constraint on the fluid velocity and the positivity of the density, pressure and specific internal energy. Preserving these constraints is very important for robust computations, otherwise violating one of them will lead to the ill-posed problem and numerical instability. To overcome the difficulties arising from the inherent strong nonlinearity contained in the constraints, we derive an equivalent definition of the admissible states. Using this definition, we prove the convexity, scaling invariance and LaxFriedrichs (LxF) splitting property of the admissible state set G, and discover the dependence of G on the spacetime metric. Unfortunately, such dependence yields the non-equivalence of G at different points in curved spacetime, and invalidates the convexity of G in analyzing PCP schemes. This obstacle is effectively overcame by introducing a new formulation of the GRHD equations. Based on this formulation and the above theories, a first-order LxF scheme is designed on general unstructured mesh and rigorously proved to be PCP under a CFL condition. With two types of PCP limiting procedures, we design high-order, provably (not probably) PCP methods under discretization on the proposed new formulation. These high-order methods include the PCP finite difference, finite volume and discontinuous Galerkin methods.

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Section: Pcp Flux Limitermentioning

confidence: 95%

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

2017

Phys. Rev. D

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“…The result for an equilibrium relativistic gas is given by Synge (38). We used a simple approximation, accurate to 1%, given by Ryu et al (26).…”

Section: Simulation Toolsmentioning

confidence: 99%

“…table S1. Pressures calculated from the kinetic energy density computed by the PIC simulations using the approximation by Ryu et al (26).…”

Section: Supplementary Materialsmentioning

confidence: 99%

Energy Penetration into Arrays of Aligned Nanowires Irradiated with Relativistic Intensities: Scaling to Terabar Pressures

Bargsten

Hollinger

Capeluto

et al. 2016

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Ultrahigh-energy density (UHED) matter, characterized by energy densities >1 × 10 8 J cm −3 and pressures greater than a gigabar, is encountered in the center of stars and inertial confinement fusion capsules driven by the world's largest lasers. Similar conditions can be obtained with compact, ultrahigh contrast, femtosecond lasers focused to relativistic intensities onto targets composed of aligned nanowire arrays. We report the measurement of the key physical process in determining the energy density deposited in high-aspect-ratio nanowire array plasmas: the energy penetration. By monitoring the x-ray emission from buried Co tracer segments in Ni nanowire arrays irradiated at an intensity of 4 × 10 19 W cm, we demonstrate energy penetration depths of several micrometers, leading to UHED plasmas of that size. Relativistic three-dimensional particle-in-cell simulations, validated by these measurements, predict that irradiation of nanostructures at intensities of >1 × 10 22 W cm −2 will lead to a virtually unexplored extreme UHED plasma regime characterized by energy densities in excess of 8 × 10 10 J cm −3

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“…(9); see Mignone et al (2005), Ryu et al (2006), and Mignone & McKinney (2007) for other options. In ECHO the following three inversion methods are implemented.…”

Section: Primitive Variablesmentioning

confidence: 99%

ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics

Zanna¹,

Zanotti²,

Bucciantini

et al. 2007

A&A

316

448

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Aims. We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent threedimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3 + 1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods. Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities.

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Equation of State in Numerical Relativistic Hydrodynamics

Cited by 100 publications

References 24 publications

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Energy Penetration into Arrays of Aligned Nanowires Irradiated with Relativistic Intensities: Scaling to Terabar Pressures

ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics

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