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KSME International Journal

, Volume 17, Issue 12, pp 2034–2041 | Cite as

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

  • Ho-Keun Kang
  • Michihisa Tsutahara
  • Ki-Deok Ro
  • Young-Ho Lee
Article

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.

Key Words

Computational Fluid Dynamics (CFD) Lattice Boltzmann Method (LBM) BGK Model Compressible Fluid Shock Wave Reflection Wave 

Nomenclature

c

Particle velocity

cs

Sound speed

e

Internal energy

fσi(t,r)

Particle distribution function onr att

P

Pressure

R

Radius of curvature

R*

Gas constant

r

Lattice node

T

Absolute temperature

t

Time

ua

Fluid velocity

Greek symbols

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

Subscripts

αβγ

Cartesian coordinate

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References

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2003

Authors and Affiliations

  • Ho-Keun Kang
    • 1
  • Michihisa Tsutahara
    • 2
  • Ki-Deok Ro
    • 3
  • Young-Ho Lee
    • 4
  1. 1.School of Mechanical and Aerospace Engineering, Institute of Marine IndustryGyeongsang National UniversityTongyeong, GyeongnamKorea
  2. 2.Graduate School of Science and TechnologyKobe UniversityNada, KobeJapan
  3. 3.School of Mechanical and Aerospace Engineering, Institute of Marine IndustryGyeongsang National UniversityTongyeong, GyeongnamKorea
  4. 4.Division of Mechanical & Information EngineeringKorea Maritime UniversityYoungdo-ku, BusanKorea

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