Moment-Based Acceleration for Neutral Gas Kinetics with BGK Collision Operator

In this work, we present a moment-based accelerator algorithm for a Picard iteration applied to a neutral gas dynamics Boltzmann transport equation with a Bhatnagar-Gross-Krook collision operator. Traditional approaches relying on either explicit or Picard iteration schemes (i.e., source iteration) are severely limited for investigating time-scales much larger than the collisional relaxation time-scale, tau. We have developed a nonlinear accelerator algorithm that allows one to step over this stiff collision time scale and follow the hydrodynamic time scale of the problem when appropriate. The new algorithm relies on formulating a nonlinear, coupled system comprised of a high-order (HO) kinetic equation and a low-order (LO) fluid moment equation system. The HO equation provides self-consistent closures to the LO fluid equations, while the latter provides the required implicit-moment variables to evaluate the collision operator. We characterize the performance of the new algorithm on a Sod shock tube and a strong shock tube problem with varying Knudsen number.