Lattice Boltzmann methods for fluid-dynamics in relativistic regimes / student: Alessandro Gabbana. Wuppertal, [2020]
Content
- Introduction
- 1 Relativistic Boltzmann Equation
- 1.1 Macroscopic Description
- 1.2 The laws of Navier-Stokes and Fourier
- 1.3 Relaxation Time Approximation
- 1.4 Transport Coefficients
- 1.5 Equation of State
- 2 Relativistic Lattice Boltzmann Method
- 2.1 Relativistic Lattice Boltzmann Method: a survey of early developments
- 2.2 Detour: Derivation of classical Lattice Boltzmann models
- 2.3 Towards a unified lattice kinetic scheme
- 2.4 Transport coefficients
- 2.5 Forcing Scheme
- 2.6 Relativistic Lattice Boltzmann Algorithm
- 2.7 Conversion between physics and lattice units
- 2.8 Numerical validation: The Riemann problem
- 3 Hydrodynamics of electrons in graphene
- 3.1 Current whirlpools in the vicinity-geometry
- 3.2 Nonlinearities and detection of preturbulent signals
- 4 Implementation of LBM codes on modern HPC architectures
- Conclusions and Outlook
- Appendices
- A Special Relativity
- B Useful integrals
- B.1 Integrals in (3+1) dimensions
- B.2 Integrals in (2+1) dimensions
- B.3 Integrals in (1+1) dimensions
- C Relativistic Orthogonal Polynomials
- D Relativistic Orthogonal Projections
- E Quadratures
- References