A unified gas-kinetic scheme for multiscale and multicomponent flow transport

  • Tianbai XiaoEmail author
  • Kun Xu
  • Qingdong Cai


Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme (UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time (or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments. The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.

Key words

unified gas-kinetic scheme (UGKS) multiscale modeling multicomponent flow 

Chinese Library Classification


2010 Mathematics Subject Classification

82B40 76P05 


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanics and Engineering Science, College of EngineeringPeking UniversityBeijingChina
  2. 2.Department of MathematicsHong Kong University of Science and TechnologyHong KongChina
  3. 3.Department of Mechanical and Aerospace EngineeringHong Kong University of Science and TechnologyHong KongChina
  4. 4.Shenzhen Research InstituteHong Kong University of Science and TechnologyShenzhenChina

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