The investigation of flow instability and turbulence across various speed and rarefaction conditions holds significance due to their crucial roles in both engineering applications and natural flows. While the Navier-Stokes equation effectively describes these phenomena in the continuum limit, the impact of rarefaction on instability and other flow characteristics remains inadequately understood. This talk will summarize the application of Lattice Boltzmann Method (LBM), Gas Kinetic Scheme (GKS), and Unified Gas Kinetic Scheme (UGKS) across different speed and rarefaction scenarios to gain insights into fundamental flow physics. Specifically, it explores the dependency of key phenomena on Knudsen and Mach numbers. Canonical cases, including homogeneous turbulence, Kelvin-Helmholtz instability (free shear flow), and flow within a lid-driven cavity (internal shear flow), are analyzed. The study reveals a profound influence on both instability and vortex structure as the Knudsen number increases, signifying a transition from diffusive to ballistic molecular transport. The extent of instability/vorticity modification is contingent upon the ratio of advective (convective) to molecular (ballistic) transport, expressed through dimensionless collision frequency. The research quantifies the rarefaction effects on Kelvin-Helmholtz instability across different Mach numbers, distinguishing between solenoidal and dilatational fields. Similarly, it establishes the dependence of vortex structure on Knudsen and Mach numbers within the cavity flow. Generally, as collision frequency decreases, the dominance of ballistic transport effects becomes apparent, resulting in a significant weakening of both instabilities and vortex structures.