# Towards a unified lattice kinetic scheme for relativistic hydrodynamics.

@article{Gabbana2017TowardsAU, title={Towards a unified lattice kinetic scheme for relativistic hydrodynamics.}, author={A. Gabbana and M. Mendoza and S. Succi and R. Tripiccione}, journal={Physical review. E}, year={2017}, volume={95 5-1}, pages={ 053304 } }

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and… Expand

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#### References

SHOWING 1-10 OF 41 REFERENCES

Fast lattice Boltzmann solver for relativistic hydrodynamics.

- Physics, Medicine
- Physical review letters
- 2010

This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativists outflows. Expand

Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics

- Physics
- 2010

A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010) is… Expand

Lattice Boltzmann model for ultrarelativistic flows

- Physics
- 2013

We develop a relativistic lattice Boltzmann model capable of describing relativistic fluid dynamics at ultra-high velocities, with Lorentz factors up to $\gamma \sim 10$. To this purpose, we first… Expand

Fully relativistic lattice Boltzmann algorithm

- Physics
- 2011

Starting from the Maxwell-Juettner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding,… Expand

Relativistic Lattice Boltzmann Model with Improved Dissipation

- Physics
- 2013

We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB… Expand

A relativistic relaxation-time model for the Boltzmann equation

- Physics
- 1974

Abstract A relaxation-time model is proposed for the collisions term of the relativistic Boltzmann equation for a single-component gas. The resultant equation is solved as a power series in the… Expand

Lattice Boltzmann method for relativistic hydrodynamics: Issues on conservation law of particle number and discontinuities

- Physics
- 2012

In this paper, we aim to address several important issues about the recently developed lattice Boltzmann (LB) model for relativistic hydrodynamics [M. Mendoza, B. Boghosian, H. Herrmann, and S.… Expand

Collective cyclotron motion of the relativistic plasma in graphene

- Physics
- 2008

We present a theory of the finite temperature thermoelectric response functions of graphene in the hydrodynamic regime where electron-electron collisions dominate the scattering. In moderate magnetic… Expand

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

- Physics
- 2012

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional… Expand

Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production

- Physics
- 1974

We find that the single-particle distribution EdNd3p for an expanding relativistic gas described by a distribution function obeying the Boltzmann transport equation is not of the form of an integral… Expand