BGK-based schemes for the simulation of compressible flow

K. Xu, C. Kim, L. Martinelli, A. Jameson

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Following van Leer's MUSCL idea, a numerical scheme can be regarded as consisting of two key steps: a reconstruction step followed by a gas evolution step. We present a gas-kinetic method based on the collisional BGK model which provides an alternative to Riemann solvers for the gas evolution step. An advanced BGK-scheme is derived under quite general assumptions on the initial conditions. The new formulation uses interpolation of the characteristic variables in the reconstruction step and a BGK-type flow solver in the gas evolution step. The scheme satisfies both an entropy condition and a positivity condition, which guarantees a positive density and temperature at the cell interface during a complete time step. Numerical results for one-dimensional and two-dimensional test cases are presented to show the accuracy and robustness of the proposed approach.

Original languageEnglish (US)
Pages (from-to)213-235
Number of pages23
JournalInternational Journal of Computational Fluid Dynamics
Issue number3
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Aerospace Engineering
  • Energy Engineering and Power Technology
  • Computational Mechanics


  • BGK-type flow solver
  • Characteristic reconstruction
  • Compressible flows
  • Entropy and positivity conditions


Dive into the research topics of 'BGK-based schemes for the simulation of compressible flow'. Together they form a unique fingerprint.

Cite this