Kun Xu (Hong Kong University of Science and Technology, China)   

Title: Modeling and Computation of Multi-scale Transport
Abstract: The modeling of gas dynamics spans different scales: Navier-Stokes equations describe continuum flow, while the Boltzmann equation governs rarefied flow. Although these equations operate at distinct physical scales, their numerical implementation has to be done in a discretized space with computational cell resolution. A practical example is the flow around a hypersonic vehicle in near space, where conditions vary dramatically - from highly compressible continuum flow at the leading edge to free molecular flow at the trailing edge. The cell's Knudsen number can vary by several orders of magnitude. Similar multiscale phenomena occur in radiative and neutron transfer, where optical thickness variations cause sharp transitions between free particle transport and diffusive processes.
To address these multiscale transport phenomena, we have developed the unified gas-kinetic scheme (UGKS) and unified gas-kinetic wave-particle (UGKWP) method. These approaches provide a unified framework for simulating rarefied flow, radiative and neutron transfer, and plasma physics across all flow regimes.