Particle ellipsoidal statistical bhatnagar-gross-krook approach for simulation of hypersonic shocks

Ozgur Tumuklu, Zheng Li, Deborah A. Levin

Research output: Contribution to journalArticlepeer-review


To reduce the computational costs related to direct simulation Monte Carlo computations for low Knudsen number flows, a new particle method, based on the ellipsoidal statistical Bhatnagar-Gross-Krook model of the Boltzmann equation, is investigated. In this method, a fraction of the computational particles in a cell is selected for velocity reassignment from the local Maxwellian distribution based the local collision frequency and an even smaller fraction is selected for internal mode energy reassignment based on the rotational and vibrational relaxation rates. A scaling algorithm is used to decrease the required number of particles per cell and to guarantee that the energy and momentum are conserved in each time step. The accuracy and efficiency of the ellipsoidal statistical Bhatnagar-Gross-Krook method are tested in three different test cases and the results are compared with the direct simulation Monte Carlo solution and experiment as well. The ellipsoidal statistical Bhatnagar-Gross-Krook approach is found to provide good agreement with direct simulation Monte Carlo solutions, however, a factor of 2 speed up compared with direct simulation Monte Carlo is only achieved when the collision frequency is sufficiently high.

Original languageEnglish (US)
Pages (from-to)3701-3716
Number of pages16
JournalAIAA journal
Issue number12
StatePublished - 2016

ASJC Scopus subject areas

  • Aerospace Engineering


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