On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

Harten, A.; Lax, Peter D.; Leer, Bram van

doi:10.1137/1025002

Cited by 2,938 publications

(1,762 citation statements)

References 13 publications

Supporting

Mentioning

1,744

Contrasting

Unclassified

Order By: Relevance

“…From these reconstructed variables, we can then compute the fluxes F L and F R . The approximate Riemann problem on each face is then solved by computing the HLL flux [86] …”

Section: Evolution Of the Metricmentioning

confidence: 99%

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

et al. 2013

View full text Add to dashboard Cite

Black-hole-neutron-star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the postmerger remnant are very sensitive to the parameters of the binary (mass ratio, black-hole spin, neutron star radius). In this paper, we study the impact of the radius of the neutron star and the alignment of the black-hole spin on black-hole-neutron-star mergers within the range of mass ratio currently deemed most likely for field binaries (M BH $ 7M NS ) and for black-hole spins large enough for the neutron star to disrupt (J BH =M 2 BH ¼ 0:9). We find that (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0:3M NS to 0:1M NS for changes of only 2 km in the NS radius; (ii) 0:01M -0:05M of unbound material can be ejected with kinetic energy * 10 51 ergs, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable postmerger optical and radio afterglows. (iii) Only a small fraction of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star (at best $3% of the events for a single detector at design sensitivity). (iv) A misaligned black-hole spin works against disk formation, with less neutron-star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks v kick * 300 km=s can be given to the final black hole as a result of a precessing black-hole-neutron-star merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

show abstract

“…From these reconstructed variables, we can then compute the fluxes F L and F R . The approximate Riemann problem on each face is then solved by computing the HLL flux [86] …”

Section: Evolution Of the Metricmentioning

confidence: 99%

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

et al. 2013

View full text Add to dashboard Cite

show abstract

“…This formulation, used together with the Harten-Lax-van Leer approximate Riemann solver (Harten et al 1983), conserves the divergence-free condition ∇ · B = 0. The method is a second order, unsplit, time-marching algorithm scheme controlled by the Courant-Friedrich-Levy parameter initially set to C cfl = 0.1.…”

Section: Boundary Conditions and Numerical Schemementioning

confidence: 99%

Bow shock nebulae of hot massive stars in a magnetized medium

Meyer

Mignone

Kuiper

et al. 2016

Mon. Not. R. Astron. Soc.

View full text Add to dashboard Cite

A significant fraction of OB-type, main-sequence massive stars are classified as runaway and move supersonically through the interstellar medium (ISM). Their strong stellar winds interact with their surroundings where the typical strength of the local ISM magnetic field is about 3.5-7 µG, which can result in the formation of bow shock nebulae. We investigate the effects of such magnetic fields, aligned with the motion of the flow, on the formation and emission properties of these circumstellar structures. Our axisymmetric, magneto-hydrodynamical simulations with optically-thin radiative cooling, heating and anisotropic thermal conduction show that the presence of the background ISM magnetic field affects the projected optical emission our bow shocks at Hα and [OIII] λ 5007 which become fainter by about 1-2 orders of magnitude, respectively. Radiative transfer calculations against dust opacity indicate that the magnetic field slightly diminishes their projected infrared emission and that our bow shocks emit brightly at 60 µm. This may explain why the bow shocks generated by ionizing runaway massive stars are often difficult to identify. Finally, we discuss our results in the context of the bow shock of ζ Ophiuchi and we support the interpretation of its imperfect morphology as an evidence of the presence of an ISM magnetic field not aligned with the motion of its driving star.

show abstract

“…We use the HLL (Harten, Lax, and van Leer) approximate Riemann solver [52]. The HLL solver is one of the simplest shock-capturing schemes as it does not require knowledge of the eigenvectors of the system.…”

Section: B the Riemann Solver Stepmentioning

confidence: 99%

Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

et al. 2005

View full text Add to dashboard Cite

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.

show abstract

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

Cited by 2,938 publications

References 13 publications

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

Bow shock nebulae of hot massive stars in a magnetized medium

Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Contact Info

Product

Resources

About