Lattice boltzmann method for compressible flows with high mach numbers

Area of Science:

• Computational fluid dynamics
• Fluid dynamics
• Computational physics

Background:

• Lattice Boltzmann methods are widely used for fluid simulations.
• Simulating compressible flows, especially at high Mach numbers, presents significant computational challenges.
• Existing models often struggle with stability and accuracy for high Mach number regimes.

Purpose of the Study:

• To introduce a novel lattice Boltzmann model for simulating compressible flows.
• To enhance the capability of lattice Boltzmann methods to handle high Mach number flows.
• To validate the model's effectiveness through established benchmarks.

Main Methods:

• Development of a lattice Boltzmann model incorporating an attractive force term.
• Effective softening of the sound speed within the model.
• Simulation of the Mach cone phenomenon.
• Comparison of simulation results with theoretical predictions.

Main Results:

• The model successfully simulates compressible flows up to Mach 5.
• The introduced attractive force effectively softens the sound speed.
• Simulations of the Mach cone demonstrate good agreement with theoretical expectations.
• The method proves effective for high Mach number flow simulations.

Conclusions:

• The proposed lattice Boltzmann model is a viable and effective approach for simulating high Mach number compressible flows.
• The model's simplicity and effectiveness offer a promising tool for future research and applications in fluid dynamics.
• This advancement facilitates the study of phenomena previously difficult to simulate.