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Comparison of the interpolated bounce-back and immersed boundary methods

Outline. Lattice Boltzmann method with multi-relaxation-time collisionImmersed boundary lattice Boltzmann methodInterpolated bounce back schemeNumerical simulation results and analysisConclusion. LBM with MRT collision. where are moments of the distribution

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Comparison of the interpolated bounce-back and immersed boundary methods

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    1. Comparison of the interpolated bounce-back and immersed boundary methods Yan Peng Dept. Math. & Stat., Old Dominion University

    2. Outline Lattice Boltzmann method with multi-relaxation-time collision Immersed boundary lattice Boltzmann method Interpolated bounce back scheme Numerical simulation results and analysis Conclusion

    3. LBM with MRT collision where are moments of the distribution functions . is the collision matrix. M is the transformation matrix.

    4. LBM with MRT collision (cont.) In this study, D2Q9 model is used. The matrix M has the form as

    5. Immersed boundary LBM Treat the boundary as deformable with high stiffness. Small distortion yield a force to restore the boundary into original shape. The force is distributed to the flow field.

    6. Immersed boundary LBM (cont.) For immersed boundary method, the body force term is used to mimic the presence of boundary. Direct forcing scheme.

    7. Immersed boundary LBM (cont.) Execute forcing term in two steps Half before relaxation Another half during the relaxation

    8. Immersed boundary LBM (cont.) Drag and lift

    9. Immersed boundary LBM (cont.) Process for IBM-LBM 1) Compute the force density at boundary points Spread these force into flow field 2) Solve the lattice Boltzmann equation with force term 3) Interpolate the velocity to the boundary points Go back to the first step

    10. Interpolated bounce back

    11. Interpolated bounce back (cont.) Quadratic interpolation is used

    12. Interpolated bounce back (cont.) Momentum transfer method

    13. Application of these two methods

    14. Flow past the Circular Cylinder (Re=20)

    15. Flow past the Circular Cylinder (cont.)

    16. Flow past the Circular Cylinder (cont.)

    17. Flow past the Circular Cylinder (cont.)

    18. Flow past the Circular Cylinder (cont.)

    19. Flow past the Circular Cylinder (cont.)

    20. Flow past the Circular Cylinder (cont.)

    21. Conclusion (Preliminary) For the same grid number, interpolation bounce back scheme obtain more accurate results than immersed boundary method To obtain accurate results, immersed boundary needs much more grids than interpolation bounce back scheme On the boundary, immersed boundary method has lower order accuracy in space than interpolation bounce back scheme

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