English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Developing extended hydrodynamics equations valid for both dense and rarefiedgases remains a great challenge. A systematical solution for this challenge isthe moment method describing both dense and rarefied gas behaviors with momentsof gas molecule velocity distributions. Among moment methods, the maximalentropy moment method (MEM) stands out for its well-posedness and stability,which utilizes velocity distributions with maximized entropy. However, findingsuch distributions requires solving an ill-conditioned andcomputation-demanding optimization problem. This problem causes numericaloverflow and breakdown when the numerical precision is insufficient, especiallyfor flows like high-speed shock waves. It also prevents modern GPUs fromaccelerating optimization with their enormous single floating-point precisioncomputation power. This paper aims to stabilize MEM, making it practical forsimulating very strong normal shock waves on modern GPUs at single precision.We propose the gauge transformations for MEM, making the optimization lessill-conditioned. We also tackle numerical overflow and breakdown by adoptingthe canonical form of distribution and Newton's modified optimization method.With these techniques, we achieved a single-precision GPU simulation of a Mach10 shock wave with 35 moments MEM, surpassing the previous double-precisionresults of Mach 4. Moreover, we argued that over-refined spatial mesh degradesboth the accuracy and stability of MEM. Overall, this paper makes the maximalentropy moment method practical for simulating very strong normal shock waveson modern GPUs at single-precision, with significant stability improvementcompared to previous methods.

Stabilizing the Maximal Entropy Moment Method for Rarefied Gas Dynamics at Single-Precision