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Moment gas kinetic flux solver for simulation of flows from continuum regime to rarefied regime

Zhenyu Yuan (袁震宇)1 and Chang Shu (舒昌)2,*

  • *Contact author: mpeshuc@nus.edu.sg
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Phys. Rev. Fluids 11, 063401 – Published 22 June, 2026

DOI: https://doi.org/10.1103/2grk-9fqf

Abstract

This paper proposes the moment gas kinetic flux solver (MGKFS) for the simulation of flows from a continuum regime to a rarefied regime. Its fundamental innovation lies in the dual-flux strategy, which extends the conventional gas kinetic flux solver (GKFS) paradigm by directly calculating numerical fluxes not only for the conservation equations (mass, momentum, and energy) but also for the high-order moment equations (stress and heat flux) at cell interfaces. Thus, MGKFS effectively overcomes the critical limitation identified in the Grad-13-based GKFS (G13-GKFS). G13-GKFS locally interpolates stress and heat flux at cell centers from their values at cell interfaces. This approach neglects their global evolution equations, leading to insufficient global accuracy. MGKFS directly captures the evolution of these high-order moments with flux reconstruction from the local solution of the Boltzmann equation at the cell interface. Numerical validations demonstrate that MGKFS significantly outperforms G13-GKFS, achieving superior accuracy. This improvement is particularly notable in boundary layers, where global fidelity is essential.

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Information

Phys. Rev. Fluids 11, 063401– Published 22 June, 2026
  • Received 30 August 2025
  • Accepted 17 April 2026
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