Papers › Stabilizing the Maximal Entropy Moment Method for Rarefied Gas Dynamics at Single-Precision
Stabilizing the Maximal Entropy Moment Method for Rarefied Gas Dynamics at Single-Precision
Candi Zheng, Wang Yang, Shiyi Chen
The maximal entropy moment method (MEM) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. However, simulating MEM suffers from a computational expensive and ill-conditioned maximal entropy problem. It causes numerical overflow and breakdown when the numerical precision is insufficient, especially for flows like high-speed shock waves. It also prevents modern GPUs from accelerating MEM with their enormous single floating-point precision computation power. This paper aims to stabilize MEM, making it possible to simulating very strong normal shock waves on modern GPUs at single precision. We improve the condition number of the maximal entropy problem by proposing gauge transformations, which moves not only flow fields but also hydrodynamic equations into a more optimal coordinate system. We addressed numerical overflow and breakdown in the maximal entropy problem by employing the canonical form of distribution and a modified Newton optimization method. Moreover, we discovered a counter-intuitive phenomenon that over-refined spatial mesh beyond mean free path degrades the stability of MEM. With these techniques, we accomplished single-precision GPU simulations of high speed shock wave up to Mach 10 utilizing 35 moments MEM, while previous methods only achieved Mach 4 on double-precision.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections