A unified implicit scheme for kinetic model equations. Part I. Memory reduction technique.

Area of Science:

• Computational Physics
• Numerical Analysis
• Fluid Dynamics

Background:

• Solving kinetic equations requires substantial memory due to storing distribution functions.
• Existing methods face limitations in memory efficiency for complex simulations.

Purpose of the Study:

• To develop a memory reduction technique for stationary kinetic model equations.
• To introduce an implicit numerical method that alleviates memory requirements.

Main Methods:

• Reconstructing the velocity distribution function from macroscopic variables at a discrete level.
• Developing an implicit numerical method that stores only macroscopic quantities for the collision term.
• Implementing and testing various boundary conditions (inlet, outlet, isothermal).

Main Results:

• The proposed implicit method drastically reduces memory usage for kinetic equation solvers.
• Numerical tests confirm the validity and efficiency of the memory reduction technique.
• The new solver achieves nearly identical solutions to explicit methods with significantly lower memory footprint.

Conclusions:

• The developed technique effectively relieves the enormous memory requirements for solving kinetic equations.
• This implicit solver offers a memory-efficient alternative, comparable to Navier-Stokes solvers.
• The method is validated for various boundary conditions, demonstrating broad applicability.