Relativistic resistive dissipative magnetohydrodynamics from the relaxation time approximation

Panda, Ankit Kumar; Dash, Ashutosh; Biswas, Rajesh; Roy, Victor

doi:10.1103/physrevd.104.054004

Cited by 22 publications

(12 citation statements)

References 37 publications

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“…The value of W determines how strongly the smoothness of the candidate ENO stencils impacts the nonlinear weights; small values of W imply strong sensitivity to nonsmoothness, and large values imply insensitivity (and as a result give a fixed fourth-order derivative stencil). Hence, for smaller W one finds larger violations of the constraint (42), which converge away with resolution (the solid lines range over Nx = 2 7 , 2 8 , 2 9 , with lighter shades representing higher resolutions). In the W → ∞ limit, constraint violation approaches machine precision (cf.…”

Section: D Oblique Shockwavementioning

confidence: 95%

“…It is straightforward to show that discretizations of (42) with fixed stencils, e.g. ∂ x X ≈ (X i+1,j − X i−1,j )/(2h) and its analogy with i → j for ∂ y X, satisfy (42) exactly.…”

Section: Reconstructionmentioning

confidence: 99%

“…∂ x X ≈ (X i+1,j − X i−1,j )/(2h) and its analogy with i → j for ∂ y X, satisfy (42) exactly. For the CWENO scheme, however, constraints like (42) are only satisfied up to truncation error in the solution, here O(h 2 ). That said, for large values of the WENO/CWENO parameter W the derivatives approach those coming from a fixed stencil, and violations of (42) vanish; for a thorough exploration of curl-type constraint violation for the BDNK scheme, see Sec.…”

Section: Reconstructionmentioning

confidence: 99%

“…Frame complications also cause problems for physical scenarios relevant to astrophysics: MIS breaks down when sufficiently strong (high Mach number) shockwaves form [36], whereas arbitrarily strong shockwave solutions exist in BDNK theory for well-chosen frames [1] [37]. On the other hand, astrophysical problems, by and large, require the consistent inclusion of magnetic fields into the evolution, which is currently only known for MIS-type dissipative theories [38][39][40][41][42]. Despite the lack of causality constraints, such theories have been successfully used in astrophysical studies [43,44].…”

Section: Introductionmentioning

confidence: 99%

“…FIG.3. Integral of the absolute value of the constraint(42) over the domain for viscous rotor initial data with η0 = 0.2. The value of W determines how strongly the smoothness of the candidate ENO stencils impacts the nonlinear weights; small values of W imply strong sensitivity to nonsmoothness, and large values imply insensitivity (and as a result give a fixed fourth-order derivative stencil).…”

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confidence: 99%

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Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

Pandya,

Most,

Pretorius

2022

Preprint

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We present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising means of incorporating entropy-generating effects (viscosity, heat conduction) into relativistic fluid models, appearing as a possible alternative to the so-called Müller-Israel-Stewart (MIS) theory successfully used to model quark-gluon plasma. Both BDNK and MIS-type theories may be understood in terms of a gradient expansion about the perfect (ideal) fluid, wherein BDNK arises at first order and MIS at second order. As such, BDNK has vastly fewer terms and undetermined model coefficients (as is typical for an effective field theory appearing at lower order), allowing for rigorous proofs of stability, causality, and hyperbolicity in full generality which have as yet been impossible for MIS. To capitalize on these advantages, we present the first fully conservative multi-dimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, non-oscillatory reconstruction, and a central-upwind numerical flux, and is designed to smoothly transition to a high-resolution shock-capturing perfect fluid solver in the inviscid limit. We assess the robustness of our new method in a series of flat-spacetime tests for a conformal fluid, and provide a detailed comparison with previous approaches of Pandya & Pretorius (2021) [1].

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Section: D Oblique Shockwavementioning

confidence: 95%

Section: Reconstructionmentioning

confidence: 99%

Section: Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

Pandya,

Most,

Pretorius

2022

Preprint

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Order-by-order anisotropic transport coefficients of a magnetised fluid: a Chapman-Enskog approach

Gangopadhyaya

Roy

2022

J. High Energ. Phys.

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We derive the first and second-order expressions for the shear, the bulk viscosity, and the thermal conductivity of a relativistic hot boson gas in a magnetic field using the relativistic kinetic theory within the Chapman-Enskog method. The order-by-order off-equilibrium distribution function is obtained in terms of the associate Laguerre polynomial with magnetic field-dependent coefficients using the relativistic Boltzmann-Uehling-Uhlenbeck transport equation. The order-by-order anisotropic transport coefficients are evaluated in powers of the dimensionless ratio of kinetic energy to the fluid temperature for finite magnetic fields. In a magnetic field, the shear viscosity (in all order) splits into five different coefficients. Four of them show a magnetic field dependence as seen in a previous study [1] using the relaxation time approximation for the collision kernel. On the other hand, bulk viscosity, which splits into three components (in all order), is independent of the magnetic field. The thermal conductivity shows a similar splitting but is field-dependent. The difference in the first and second-order results are prominent for the thermal conductivities than the shear viscosity; moreover, the difference in the two results is most evident at low temperatures. The first and second-order results seem to converge rapidly for high temperatures.

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Charged participants and their electromagnetic fields in an expanding fluid

Dash,

Panda

2024

Physics Letters B

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Relativistic resistive dissipative magnetohydrodynamics from the relaxation time approximation

Cited by 22 publications

References 37 publications

Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

Order-by-order anisotropic transport coefficients of a magnetised fluid: a Chapman-Enskog approach

Charged participants and their electromagnetic fields in an expanding fluid

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