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Lattice Boltzmann method for compressible Euler equations based on exact kinetic system
Author(s) -
Hanada Takaya,
Kataoka Takeshi
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4987
Subject(s) - inviscid flow , euler equations , lattice boltzmann methods , compressibility , kinetic energy , boltzmann equation , euler's formula , distribution function , supersonic speed , compressible flow , mathematics , computation , kinetic scheme , physics , classical mechanics , mathematical analysis , statistical physics , mechanics , thermodynamics , algorithm
We have developed a new type of simple lattice Boltzmann (LB) model for the compressible Euler equations based on the collisionless kinetic‐equation approach proposed by Sone. The model uses the collisionless kinetic equation in the streaming process, and modifies the distribution function to its Chapman–Enskog type at each time step. Compared with the current LB models which solve the kinetic equation of the BGK type, the proposed model is superior in the following two points: (i) Inviscid flows can be computed stably while there is no such model in the current LBM; (ii) The velocity distribution function does not need to be memorized in computation. We calculate various inviscid compressible flows described by the compressible Euler equations using our new one‐, two‐, and three‐dimensional models. Numerical results show the capability of our scheme to simulate high‐speed supersonic flows with shock waves.