Why Ultrarelativistic Numerical Hydrodynamics is Difficult

Norman, Michael L.; Winkler, Karl-Heinz A.

doi:10.1007/978-94-009-4754-2_13

Cited by 42 publications

(70 citation statements)

References 12 publications

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“…Earlier pioneer approaches in the field of relativistic hydrodynamics (Norman & Winkler 1986;Centrella & Wilson 1984) used standard finite-difference schemes in conjunction with artificial viscosity terms to stabilize the solution across discontinuities. Those approaches, however, only succeeded in obtaining accurate results for moderate values of the Lorentz factor (W ∼ 2).…”

Section: Discussionmentioning

confidence: 99%

“…W 1 ∼ 7070, corresponding to v = −0.99999999c). The most important property which allows central schemes such as the one presented here to succeed in the ultrarelativistic regime seems to be, in retrospect, the conservation form of the scheme, something which was not taken into account in the pioneer investigations in (ultra) relativistic hydrodynamics (Norman & Winkler 1986). …”

Section: Problem 5: Shock Reflection Testmentioning

confidence: 99%

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Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Lucas-Serrano

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Abstract.We assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime.Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

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Section: Discussionmentioning

confidence: 99%

Section: Problem 5: Shock Reflection Testmentioning

confidence: 99%

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Lucas-Serrano

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et al. 2004

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“…Another important point to note is that the derived energy equation, Eq. (39), does not contain destabilizing [32] time derivatives of Lorentz factors on the RHS -in contrast to the thermal energy equation (35) and to earlier SPH formulations [7]. For a practical simulation involving shocks, Eqs.…”

Section: The Energy Equationmentioning

confidence: 95%

Relativistic smooth particle hydrodynamics on a given background spacetime

Rosswog

2010

Class. Quantum Grav.

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Abstract. We review the derivation of fixed-metric, relativistic smooth particle hydrodynamics (SPH) from the Lagrangian of an ideal fluid. Combining the EulerLagrange equations with the first law of thermodynamics, we explicitely derive evolution equations for the canonical momentum and energy. This new set of SPH equations also accounts for corrective terms that result from derivatives of the SPH smoothing kernel and that are called "grad-h" terms in non-relativistic SPH. The new equations differ from earlier formulations with respect to these corrective terms and the symmetries in the SPH particle indices while being identical in the gravitational terms.Confidential: not for distribution.

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“…The density jump in the shell reaches a value of 10.4. Norman and Winkler (1986) only-) shows the evolution of the blast wave simulated with rPPM (Martí and Müller, 1996;Martí and Müller, 2003) on a grid of 2000 equidistant cells. At this resolution rPPM obtains a converged solution.…”

Section: Problemmentioning

confidence: 99%

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Martí

Müller

2015

Living Rev Comput Astrophys

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An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates. Article RevisionsLiving Reviews supports two ways of keeping its articles up-to-date:Fast-track revision. A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here.Major update. A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number.For detailed documentation of an article's evolution, please refer to the history document of the article's online version at http://dx

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Why Ultrarelativistic Numerical Hydrodynamics is Difficult

Cited by 42 publications

References 12 publications

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Relativistic smooth particle hydrodynamics on a given background spacetime

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

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