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Shock wave profiles in the burnett approximation

Uribe1, Velasco, Garcia-Colin

  • 1Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico Distrito Federal, Mexico.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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This study investigates shock wave profiles in gases using nonlinear Burnett equations. Heteroclinic trajectories, crucial for understanding shock wave behavior, were found to exist for Mach numbers above 1, up to a critical point.

Area of Science:

  • Fluid Dynamics
  • Kinetic Theory
  • Nonlinear Hydrodynamics

Background:

  • Shock waves are fundamental phenomena in fluid dynamics.
  • Understanding shock wave profiles requires advanced kinetic theory.
  • The Burnett equations offer a more complete description than Navier-Stokes.

Purpose of the Study:

  • To analyze shock wave profiles using nonlinear Burnett equations.
  • To investigate the existence of heteroclinic trajectories in shock waves.
  • To compare numerical solutions with the Direct Simulation Monte Carlo method.

Main Methods:

  • Chapman-Enskog solution to the Boltzmann equation.
  • Numerical analysis via transformation into first-order equations.
  • Adam's method for solving Burnett equations.

Related Experiment Videos

  • Comparison with Direct Simulation Monte Carlo (DSMC) method.

    • Main Results:

    • Heteroclinic trajectories exist for Burnett equations at Mach numbers > 1.
    • These trajectories are found up to a critical Mach number of approximately 2.69.
    • A saddle-node-Hopf bifurcation occurs at the critical Mach number.

    Conclusions:

    • The existence of heteroclinic trajectories is confirmed for specific shock wave conditions.
    • A critical Mach number marks a bifurcation point in the system's dynamics.
    • Further research is needed to fully clarify the implications of this bifurcation.