Abstract
In this paper, a high-order/low-order (HOLO) method is combined with a micromacro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar-Gross-Krook (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 away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. The accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.
| Original language | English |
|---|---|
| Pages (from-to) | 3566-3593 |
| Number of pages | 28 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 47 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 2025 |
Funding
\ast Submitted to the journal's Numerical Algorithms for Scientific Computing section October 1, 2024; accepted for publication (in revised form) September 22, 2025; published electronically November 25, 2025. https://doi.org/10.1137/24M1698298 Funding: Notice: This manuscript has been authored by UT-Battelle, LLC under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a non-exclusive, paid up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for U.S. Government purposes. The DOE will provide public access to these results in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). Notice: This manuscript has been authored by UT-Battelle, LLC under contract DEAC05- 00OR22725 with the U.S. Department of Energy. The publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a non-exclusive, paid up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for U.S. Government purposes. The DOE will provide public access to these results in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Keywords
- BGK model
- HOLO method
- discontinuous Galerkin
- fully implicit methods
- kinetic equations
- micro-macro