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Center for Nonlinear Studies |
In this talk, we combine a high-order/low-order (HOLO) method with a micro-macro (MM) formulation to accelerate iterative solvers in fully implicit time stepping of the 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.
Host: William T. Taitano (T-5)