Gas dynamics modeling encompasses multiple scales, from the Navier-Stokes equations governing continuum flow to the Boltzmann equation describing rarefied flow. While these equations operate at fundamentally different physical scales, their numerical implementation requires discretization in computational space with finite cell resolution. This multiscale challenge is exemplified by hypersonic vehicle flow in near-space environments, where conditions range from highly compressible continuum flow at the leading edge to free molecular flow at the trailing edge, with the cell Knudsen number varying across several orders of magnitude. Analogous multiscale phenomena arise in radiative and neutron transfer, where variations in optical thickness induce sharp transitions between free particle transport and diffusive regimes. To address these multiscale transport challenges, we have developed the unified gas-kinetic scheme (UGKS) and the unified gas-kinetic wave-particle (UGKWP) method. These approaches provide a comprehensive framework for simulating transport phenomena across all flow regimes, including rarefied gas dynamics, radiative transfer, neutron transport, and plasma physics. This presentation will also discuss the extension of our multiscale methodology to the modeling and simulation of turbulent flows.

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