On High-Order, Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model
Stefan Schnake, Ph.D.
, Oak Ridge National Laboratory
Abstract:
In this talk, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) formulation to accelerate iterative solvers in fully implicit time stepping of the Bhatnagar-Gross-Krook model (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation is small and can be compressed to reduce the overall storage cost of the distribution. The accuracy and performance of the MM-HOLO method is compared to the usual HOLO method and standard source iteration on a Sod shock tube problem and a sudden heating boundary layer problem. Both HOLO and MM-HOLO methods are implemented using a discontinuous (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. The compression enabled by the MM formulation is demonstrated as a function of the collision frequency.
Speaker’s Bio:
Dr. Stefan Schnake is a research scientist in the Multiscale Methods and Dynamics Group. He received his Ph.D. in 2017 from the University of Tennessee and joined Oak Ridge National Laboratory in 2020 after a postdoctoral appointment at the University of Oklahoma. His research interests include low-rank and sparse-grid methods for compressing tensor representations of solutions to dynamical systems.
