Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats
Shingo Kosuge, Kazuo Aoki
Abstract
A system of Navier–Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the problem of shock-wave structure for a gas with large bulk viscosity (or, equivalently, with slow relaxation of the internal modes), and the numerical results are compared with those based on the ordinary Navier–Stokes equations. It is shown that the latter equations fail to describe the double-layer structure of shock profiles for a gas with large bulk viscosity.
Topics & Concepts
Polyatomic ionViscosityThermodynamicsPhysicsBoltzmann equationVolume viscosityShock waveNavier–Stokes equationsRelaxation (psychology)Shock (circulatory)Perfect gasBoltzmann constantMechanicsClassical mechanicsMoleculeCompressibilityQuantum mechanicsSocial psychologyMedicineInternal medicinePsychologyGas Dynamics and Kinetic TheoryComputational Fluid Dynamics and AerodynamicsHigh-pressure geophysics and materials