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Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.
1State Key Laboratory of Multiphase Flow, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
Summary
A new lattice Boltzmann method accurately solves compressible Navier-Stokes equations. This flexible approach allows adjustable specific-heat ratios and Prandtl numbers for fluid dynamics simulations.
Area of Science:
- Computational fluid dynamics
- Fluid mechanics
- Numerical analysis
Background:
- Existing thermal lattice Boltzmann methods have limitations in recovering compressible Navier-Stokes equations with flexible parameters.
- Accurate simulation of compressible fluid flow is crucial in various engineering applications.
Purpose of the Study:
- To develop a coupled double-distribution-function lattice Boltzmann method for compressible Navier-Stokes equations.
- To enable flexible control over specific-heat ratio and Prandtl number in simulations.
Main Methods:
- A multispeed lattice density distribution function recovers continuity and momentum equations.
- An energy distribution function recovers the compressible energy equation.
- Coupling via the equation of state and introducing a specific-heat ratio constant in equilibrium energy distribution.
Main Results:
- The method successfully recovers compressible Navier-Stokes equations with adjustable specific-heat ratio and Prandtl number.
- Numerical simulations of Riemann problems, double-Mach-reflection, and Couette flow show excellent agreement with existing solutions.
- Two distinct coupled double-distribution-function lattice Boltzmann models are proposed.
Conclusions:
- The developed lattice Boltzmann method provides a robust and flexible tool for simulating compressible fluid flows.
- The method's ability to handle variable specific-heat ratios and Prandtl numbers enhances its applicability in diverse scenarios.
- The excellent agreement of numerical results validates the proposed method and its models.
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