High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases

Blaga, Robert; Ambruş, Victor E.

doi:10.1103/physrevc.98.035201

Cited by 31 publications

(74 citation statements)

References 112 publications

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“…In recent times, numerical schemes based on the Lattice Boltzmann Method (LBM) have emerged as a promising tool for the study of dissipative relativistic hydrodynamics [18,37,38,[41][42][43]47]. The advantage of this approach is that by working at a mesoscopic level viscous effects are naturally included, with relativistic invariance and causality preserved by construction.…”

Section: Relativistic Lattice Boltzmann Methodsmentioning

confidence: 99%

“…which implies, by direct comparison with Eq 27, the following expression for the bulk viscosity µ: µ = Pτ a 43…”

Section: Bulk Viscositymentioning

confidence: 99%

“…Higher orders would most probably require different strategies, e.g. off-lattice schemes, which drastically improve the spatial resolution of the grid, but have as drawbacks the need for interpolation and the introduction of artificial dissipation effects [43,47,77]; we do not consider these strategies in this paper.…”

Section: Gauss-type Quadratures With Prescribed Abscissasmentioning

confidence: 99%

“…Another significant algorithmic development was presented in [43], where the authors describe a systematic procedure to define quadrature rules at high orders, giving the possibility to go well beyond hydrodynamics and to handle flows from a strongly interacting near-inviscid regime, all the way to the ballistic regime. The model is restricted to flows of massless particles and has been so far applied only to one-dimensional flows.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed QGP in possibly the most natural field of application for RLBM methods. In this context it has been used to investigate several problems of shock waves propagation [18,36,[39][40][41][42][43][44][45] and other standard benchmarks, such as the 1-d Bjorken flow [37,43,46]. However, to the best of our knowledge, a fully-fledged implementation for simulating nuclear collisions has not been reported, as yet.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, k B T mc 2 , and the non-relativistic one, k B T mc 2 . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1, 2, 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic (k B T ∼ mc 2 ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

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Section: Relativistic Lattice Boltzmann Methodsmentioning

confidence: 99%

“…which implies, by direct comparison with Eq 27, the following expression for the bulk viscosity µ: µ = Pτ a 43…”

Section: Bulk Viscositymentioning

confidence: 99%

Section: Gauss-type Quadratures With Prescribed Abscissasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

Ambruş

Sofonea

2019

Soft and Biological Matter

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At non-negligible values of the Knudsen number Kn (defined as the ratio between the mean free path of the fluid particles in a gas and the characteristic length of the domain), the Navier-Stokes equations lose applicability [1, 2]. Such rarefied gas flows can be approached within the framework of the Boltzmann equation [3-5]. This equation describes the six-dimensional phase-space evolution of the distribution function f , where f (t, x, p)d 3 xd 3 p gives the number of particles at time t which are contained in an infinitesimal volume d 3 x centred on x, having momenta in an infinitesimal range d 3 p about p. Because of its complexity, the Boltzmann equation can be solved analytically only in a very limited number of cases. Alternatively, numerous well-established approaches to the numerical solutions of the Boltzmann equation are now currently used for academic or engineering purposes, of which we only mention the direct simulation Monte Carlo (DSMC) technique [6], the discrete velocity models (DVMs) [7-9], the discrete unified gas-kinetic scheme (DUGKS) [10-12] and the lattice Boltzmann (LB) models [13-20]. The LB models are a particular type of DVMs and are derived from the Boltzmann equation using a simplified version of the collision operator, as well as an appropriate discretisation of the momentum space, which ensure the recovery of the moments of the distribution function f up to a certain order N. Originally derived nearly 30 years ago from the lattice gas automata [17, 19, 20], the LB

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(3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density

Heinz

2020

Computer Physics Communications

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High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases

Cited by 31 publications

References 112 publications

Relativistic lattice Boltzmann methods: Theory and applications

Relativistic lattice Boltzmann methods: Theory and applications

Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

(3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density

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