Spectral Simulations of Fluid-Kinetic Flows with Nontrivial Boundary Conditions

We model flows in regimes where atomistic effects are important, but at scales where kinetic calculations are not possible, by using a unified discretization of the multispecies Boltzmann equation that is valid across near-continuum as well as kinetic-dominated regions. For simplicity, collisions are modeled with the Bhatnagar-Gross-Krook operator, although generalizations are straightforward. The highly dimensional phase space is made tractable with asymmetrically weighted Hermite basis functions providing a spectral representation of the velocity space, high order finite differences providing a conservative spatial discretization, and embedded Runge-Kutta methods providing an adaptive temporal discretization. Additional adaptivity is achieved by varying the number of terms in the spectral expansion as needed to capture the relevant physics. Because of our particular choice in basis functions, near-continuum regions require only the first few spectral coefficients, while regions with strong kinetic effects require more terms in the expansion. We demonstrate the physics capabilities on several canonical test cases, including with nontrivial boundary conditions, such as Maxwell's diffuse walls.