Discrete unified gas kinetic scheme for continuum compressible flows

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Kinetic theory

Background:

• Compressible gas flows require accurate numerical methods for simulation.
• Existing methods may face computational challenges with high efficiency.
• The total energy kinetic model provides a basis for developing advanced schemes.

Purpose of the Study:

• To propose a discrete unified gas kinetic scheme (DUGKS) for continuum compressible gas flows.
• To enhance the computational efficiency of simulating gas dynamics.
• To accurately recover the compressible Navier-Stokes equations.

Main Methods:

• The study employs a discrete unified gas kinetic scheme (DUGKS) based on the total energy kinetic model.
• A double distribution function formulation is used, with separate functions for mass/momentum and energy transport.
• Hermite polynomial expansions and Gauss-Hermite quadratures discretize velocity spaces.

Main Results:

• The proposed DUGKS accurately recovers the compressible Navier-Stokes equations.
• The use of seventh and fifth Gauss-Hermite quadratures significantly improves computational efficiency.
• This approach requires fewer discrete velocities compared to previous methods.

Conclusions:

• The developed DUGKS offers a computationally efficient and accurate method for compressible gas flow simulations.
• This scheme represents a specialized finite-volume lattice Boltzmann method for fluid dynamics.
• The improved efficiency makes it suitable for complex gas dynamics problems.