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Lattice kinetic algorithms for relativistic flows : a unified treatment / Daniele Simeoni. Wuppertal, 15 Dezember 2021
Content
Erklärungen
Danksagung
Kurzfassung
Contents
Introduction
Relativistic Hydrodynamics
Relativistic Kinetic Theory
Model Equations
Ideal Relativistic Hydrodynamics
Fields at Equilibrium
Equilibrium distribution function
Ideal Equation of State
Dissipative Effects
Eckart Decomposition
Landau-Lifshitz Decomposition
Transport Equations
Lattice Kinetic Schemes
Non relativistic Lattice Boltzmann Methods
Relativistic Lattice Boltzmann Methods
Expansion of the Maxwell-Jüttner distribution
Quadrature Rule for momentum discretization
Forcing Scheme
Conversion to Lattice Units
Algorithm
Derivation and Calibration of Transport Coefficients
Chapman-Enskog expansion
Grad's Method of Moments
Calibration of Transport Coefficients
Thermal Conductivity
Bulk Viscosity
Shear Viscosity
Numerical Benchmarks
Bjorken Flow
Milne coordinates
Analytic Solution (ideal ultra-relativistic fluid)
RLBM results
Mono-dimensional Shock Wave
Analytic Solution (ideal ultra-relativistic fluid)
RLBM results
Extension of the model to Weakly Interacting Regimes
Momentum Space Discretization
(2+1) dimensions
(3+1) dimensions
Decoupling of radial and angular quadratures
Mono-dimensional Shock wave
Analytic Solution (free streaming ultra-relativistic fluid)
RLBM results
Relativistic Lattice Boltzmann Method for Radiative Transfer
Theoretical Background
RLBM method
Simulation of a relativistic jet
Conclusions and Outlook
Appendices
Projector
Integrals of the Maxwell-Jüttner distribution
Integrals Z1 …n
Integrals K1 …n
List of Figures
Bibliography