PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
- Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
- OSTI ID:
- 22520176
- Journal Information:
- Astrophysical Journal, Supplement Series, Vol. 219, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0067-0049
- Country of Publication:
- United States
- Language:
- English
Similar Records
On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics
A silicon compiler for dedicated mathematical systems based on CORDIC arithmetic processors
Related Subjects
GENERAL PHYSICS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ALGORITHMS
BESSEL FUNCTIONS
BOLTZMANN STATISTICS
EQUATIONS OF STATE
FERMI STATISTICS
HYDRODYNAMICS
ISENTROPIC PROCESSES
PADE APPROXIMATION
POLYNOMIALS
RELATIVISTIC RANGE
SEMICLASSICAL APPROXIMATION
SOUND WAVES
SPECIFIC HEAT