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Numerical analysis of a weak shock wave propagating in a medium using lattice boltzmann method (LBM)

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Abstract

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method,a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles θw. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.

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Abbreviations

c :

Particle velocity

c s :

Sound speed

e :

Internal energy

f σi (t,r) :

Particle distribution function onr att

P :

Pressure

R :

Radius of curvature

R* :

Gas constant

r :

Lattice node

T :

Absolute temperature

t :

Time

u a :

Fluid velocity

γ :

Coefficient of specific heats

ɛ :

Knudsen number

X :

Thermal conductivity

λ :

Second viscosity

μ :

Viscosity

ρ :

Density

σ :

Number of speeds of particles

τ :

Time increment

φ :

Relaxation parameter

Ω :

Collision operator

αβγ:

Cartesian coordinate

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Institute of Marine Industry, Gyeongsang National University, 445 Inpyeong-dong, 650-160, Tongyeong, Gyeongnam, Korea

    Ho-Keun Kang

  2. Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai, 657-8051, Nada, Kobe, Japan

    Michihisa Tsutahara

  3. School of Mechanical and Aerospace Engineering, Institute of Marine Industry, Gyeongsang National University, 445 Inpyeong-dong, 650-160, Tongyeong, Gyeongnam, Korea

    Ki-Deok Ro

  4. Division of Mechanical & Information Engineering, Korea Maritime University, 1 Dongsam-dong, 606-791, Youngdo-ku, Busan, Korea

    Young-Ho Lee

Authors
  1. Ho-Keun Kang
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  2. Michihisa Tsutahara
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  3. Ki-Deok Ro
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  4. Young-Ho Lee
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Correspondence to Ho-Keun Kang.

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Kang, HK., Tsutahara, M., Ro, KD. et al. Numerical analysis of a weak shock wave propagating in a medium using lattice boltzmann method (LBM). KSME International Journal 17, 2034–2041 (2003). https://doi.org/10.1007/BF02982444

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  • DOI: https://doi.org/10.1007/BF02982444

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