A Flux-Split Algorithm Applied to Relativistic Flows

Donat, Rosa; Font, José A.; Ibáñez, Javier; Marquina, Antonio

doi:10.1006/jcph.1998.5955

Cited by 135 publications

(178 citation statements)

References 22 publications

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“…as in the Donat et al (1998) paper. The first test is only mildly relativistic, while the second is more severe, with a shock speed corresponding to γ 6.…”

Section: One-dimensional Testsmentioning

confidence: 80%

“…Over the last decade, high resolution shock-capturing methods of the Godunov type, successfully applied in classical fluid dynamics, have started to be employed for the case of relativistic hydrodynamics as well (Marquina et al 1992;Schneider et al 1993;Balsara 1994;Duncan & Hughes 1994;Eulderink & Mellema 1994;Font et al 1994;Dolezal & Wong 1995;Falle & Komissarov 1996;Donat et al 1998;Aloy et al 1999). These schemes are characterized by the following main features: a conservative form of the discretized equations, in order to capture weak solutions and satisfy jump relations; a reconstruction phase, to recover variables at inter-cell locations where fluxes have to be computed; an upwind phase, in which an exact or approximate solution to the local Riemann problem is found.…”

Section: Introductionmentioning

confidence: 99%

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An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Zanna

Bucciantini

Londrillo

2002

A&A

223

275

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Abstract. Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive variables and to the consequent complexity of the Jacobian matrices (needed for the spectral decomposition in most of the approximate Riemann solvers of common use). Here an efficient and easy-to-implement three-dimensional (3-D) shockcapturing scheme for ideal RHD is presented. Based on the algorithms developed by P. Londrillo & L. Del Zanna (2000, ApJ, 530, 508) for the non-relativistic magnetohydrodynamic (MHD) case, and having in mind its relativistic MHD extension (to appear in a forthcoming paper), the scheme uses high order (third) Convex Essentially Non-Oscillatory (CENO) finite difference interpolation routines and central-type averaged Riemann solvers, which do not make use of time-consuming characteristic decomposition. The scheme is very efficient and robust, and it gives results comparable to those obtained with more sophisticated algorithms, even in ultrarelativistic multidimensional test problems.

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“…as in the Donat et al (1998) paper. The first test is only mildly relativistic, while the second is more severe, with a shock speed corresponding to γ 6.…”

Section: One-dimensional Testsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Zanna

Bucciantini

Londrillo

2002

A&A

223

275

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“…mrgenesis uses a third order total variation diminishing Runge-Kutta scheme (Shu & Osher 1988) for the time integration and the piecewise-parabolic method (PPM; Colella & Woodward 1984) for the spatial interpolation. The intercell fluxes are computed with the Marquina flux formula (Donat et al 1998). The fluids are assumed to obey the ideal gas equation of state with the adiabatic index 5/3.…”

Section: Technical Detailsmentioning

confidence: 99%

Modelling accretion disc and stellar wind interactions: the case of Sgr A*

Christie

Πετροπούλου

Mimica

et al. 2016

Mon. Not. R. Astron. Soc.

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Sgr A* is an ideal target to study low-luminosity accreting systems. It has been recently proposed that properties of the accretion flow around Sgr A* can be probed through its interactions with the stellar wind of nearby massive stars belonging to the S-cluster. When a star intercepts the accretion disk, the ram and thermal pressures of the disk terminate the stellar wind leading to the formation of a bow shock structure. Here, a semi-analytical model is constructed which describes the geometry of the termination shock formed in the wind. With the employment of numerical hydrodynamic simulations, this model is both verified and extended to a region prone to Kelvin-Helmholtz instabilities. Because the characteristic wind and stellar velocities are in ∼ 10 8 cm s −1 range, the shocked wind may produce detectable X-rays via thermal bremsstrahlung emission. The application of this model to the pericenter passage of S2, the brightest member of the S-cluster, shows that the shocked wind produces roughly a month long X-ray flare with a peak luminosity of L ≈ 4 × 10 33 erg s −1 for a stellar mass-loss rate, disk number density, and thermal pressure strength ofṀ w = 10 −7 M yr −1 , n d = 10 5 cm −3 , and α = 0.1, respectively. This peak luminosity is comparable to the quiescent X-ray emission detected from Sgr A* and is within the detection capabilities of current X-ray observatories. Its detection could constrain the density and thickness of the disk at a distance of ∼ 3000 gravitational radii from the supermassive black hole.

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“…RHD codes based on upwind schemes are able to capture sharp discontinuities robustly in complex flows, and to describe the physical solution reliably. A partial list of such codes includes Falle & Komissarov (1996) based on the van Leer scheme; Martí & Müller (1996), Aloy et al (1999), and based on the piecewise parabolic method (PPM) scheme; Sokolov et al (2001) based on the Godunov scheme; Choi & Ryu (2005) based on the TVD scheme; Dolezal & Wong (1995), Donat et al (1998), DelZanna & Bucciantini (2002);and Rahman & Moore (2005) based on the essentially nonoscillatory (ENO) scheme; and based on the Harten, Lax, and van Leer (HLL) scheme. Reviews of some numerical approaches and test problems can be found in Martí & Müller (2003) and Wilson & Mathews (2003).…”

Section: Introductionmentioning

confidence: 99%

Equation of State in Numerical Relativistic Hydrodynamics

Ryu

Chattopadhyay

Choi

2006

ASTROPHYS J SUPPL S

100

158

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Relativistic temperature of gas raises the issue of the equation of state (EOS) in relativistic hydrodynamics. We study the EOS for numerical relativistic hydrodynamics, and propose a new EOS that is simple and yet approximates very closely the EOS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EOSs considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EOS, in a way that they can be used to build numerical codes. Tests with a code based on the total variation diminishing (TVD) scheme are presented to highlight the differences induced by different EOSs.

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A Flux-Split Algorithm Applied to Relativistic Flows

Cited by 135 publications

References 22 publications

An efficient shock-capturing central-type scheme for multidimensional relativistic flows

An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Modelling accretion disc and stellar wind interactions: the case of Sgr A*

Equation of State in Numerical Relativistic Hydrodynamics

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