Acta Mechanica Sinica

, Volume 33, Issue 4, pp 733–741 | Cite as

A gas-kinetic theory based multidimensional high-order method for the compressible Navier–Stokes solutions

Research Paper


This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed. However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the second-order flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.


Discontinuous Galerkin Two-stage temporal discretization Gas-kinetic theory 



The current work is supported by HKUST research fund PROVOST 13SC01.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Mathematics, School of ScienceThe Hong Kong University of Science and TechnologyHong KongChina
  3. 3.Department of Mechanical and Aerospace Engineering, School of EngineeringThe Hong Kong University of Science and TechnologyHong KongChina

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