Lattice Kinetic Theory in a Comoving Galilean Reference Frame.

Area of Science:

• Computational fluid dynamics
• Numerical methods for fluid flow

Background:

• The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid dynamics.
• Current LBM implementations face limitations in operating range, particularly for high-speed gas dynamics.

Purpose of the Study:

• To prove the Galilean invariance of the fully discrete lattice Boltzmann method.
• To introduce a novel class of shifted lattices for LBM.
• To extend the applicability of LBM to a broader range of flow regimes.

Main Methods:

• Mathematical proof of Galilean invariance for the fully discrete LBM.
• Development and implementation of a new class of shifted lattice structures.
• Numerical simulation of vortex-shock interaction to validate the proposed method.

Main Results:

• The fully discrete lattice Boltzmann method is demonstrated to be invariant under Galilean transformations.
• The proposed shifted lattices significantly expand the operational range of LBM simulations.
• Accurate and efficient simulation of vortex-shock interaction is achieved using the novel lattices.

Conclusions:

• The Galilean invariance finding unlocks broader applications for LBM.
• Shifted lattices provide a unified approach for simulating diverse flow regimes, including low, transonic, and supersonic flows.
• This advancement offers a single, versatile algorithm for a wide spectrum of gas dynamics problems.