Shock and Boundary Structure Formation by Spectral-Lagrangian Methods for the Inhomogeneous Boltzmann Transport Equation

The numerical approximation of the Spectral-Lagrangian scheme developed by the authors in Recognizing that the Boltzmann equation is an important tool in the analysis of formation of shock and boundary layer structures, we present the computational algorithm in Section 3.3 and perform a numerical study case in shock tube geometries well modeled in for 1D in x times 3D in v in Section 4. The classic Riemann problem is numerically analyzed for Knudsen numbers close to continuum. The shock tube problem of Aoki et al We consider the problem of heat transfer between two parallel plates with diffusive boundary conditions for a range of Knudsen numbers from close to continuum to a highly rarefied state. Finally, the classical infinite shock tube problem that generates a non-moving shock wave is studied. The point worth noting in this example is that the flow in the final case turns from a supersonic flow to a subsonic flow across the shock.