Mixed-regime computational fluid dynamics using the moving boundary truncated grid method for the Boltzmann-Bhatnagar-Gross-Krook model

We present an advanced moving boundary truncated grid method tailored to solve the Boltzmann-Bhatnagar-Gross-Krook equation for applications in computational fluid dynamics, emphasizing efficiency in multi-scale and rarefied gas dynamics. The truncated grid approach dynamically constrains computational resources to a significant, evolving sub-region of the phase space, allowing a targeted and computationally economical integration of the kinetic equation. First, accuracy of the truncated grid method is validated by modeling the relaxation dynamics of a rarefied gas, where the phase-space density evolution aligns excellently with the full grid reference solution but at a fraction of the computational cost. Extending the truncated grid approach to a mixed-regime problem, the solver captures transitions across the Euler, Navier-Stokes, and kinetic regimes within a far-from-equilibrium setting, yielding phase-space distributions and hydrodynamic variables that match benchmark solutions obtained with high-order schemes. Comparisons with full grid schemes underscore computational advantages of the truncated grid method, notably reducing the number of grid points without compromising solution accuracy. This study solidifies the truncated grid method as a versatile, high-performance tool for computational fluid dynamics.