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Lattice Boltzmann Simulations of Triagular Cavity Flow and Free-Surface Problems

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Abstract

The Lattice Boltzmann Method (LBM) was investigated to solve triangular cavity flow and free-surface problems in hydraulic dynamics. Some cases of triangular cavity flow and backward step flow were simulated to show the efficiency and stability of this method. Two-dimensional partial dam breaking problem and the propagation and diffraction of dam-break wave around rectangular and circular cylinder were numerically studied successfully. Excellent agreement was obtained between numerical predictions and available results.

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References

  1. BENZI R., SUCCI S., VERGASSOLA M. The lattice Boltzmann equation: theory and applications [J]. Phys. Report., 1992, 222: 145–197.

    Article  Google Scholar 

  2. QIAN Y., SUCCI S. and ORSZAG S. Recent advances in lattice Boltzmann computing [J]. Annu. Rev. Comput. Phys., 1995, 3: 195–242.

    Article  MathSciNet  Google Scholar 

  3. CHEN SHI-YI, DOOLEN G. Lattice Boltzmann method for fluid flows[J]. Annu. Rev. Fluid Mech., 1998, 30: 329–364.

    Article  MathSciNet  Google Scholar 

  4. LIN JIAN-zHONG. Research on the cylindrical particulate flows [J]. Journal of Hydrodynamics, Ser. B, 2005, 17 (1): 1–11.

    MathSciNet  MATH  Google Scholar 

  5. HE XIAO-yI, LUO LI-sHI. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation[J]. Phys. Rev. E, 1997, 56: 6811–6817.

    Article  Google Scholar 

  6. HOU SHU-lING, ZOU QI-sU, CHEN SHI-YI et al. Simulation of cavity flow by the lattice Boltzmann method[J]. J. Comput. Phys., 1995, 118: 329–347.

    Article  Google Scholar 

  7. HE XIAO-YI, DOOLEN G. D. and CLARK T. Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier-Stokes equations[J]. J. Comput. Phys., 2002, 179: 439–451.

    Article  MathSciNet  Google Scholar 

  8. GUERMOND J. L., QUARTAPELLE L. Calculation of incompressible viscous flows by an unconditional stable projection FEM[J]. J. Comput. Phys., 1997, 132: 12–33.

    Article  MathSciNet  Google Scholar 

  9. RIBBENS C. J., WATSON L. T. and WANG C. Y. Steady viscous flow in a triangular cavity[J]. J. Comput. Phys., 1994, 112: 173–181.

    Article  Google Scholar 

  10. JYOSNA R., VANKA S. P. Multigrid calculation of steady viscous flow in a triangular cavity[J]. J. Comput. Phys., 1995, 122: 107–117.

    Article  Google Scholar 

  11. LI M., TANG T. Steady viscous flow in a triangular cavity by efficient numerical techniques[J]. Comput. Math. Appl., 1996, 31: 55–65.

    Article  MathSciNet  Google Scholar 

  12. BHATNAGAR P. L., GROSS E. P. and KROOK M. A model for collision process in gas. I. Small amplitude processed in charged and neutral one component system[J]. Phys. Rev., 1954, 94: 511–525.

    Article  Google Scholar 

  13. ZHOU J. G. A lattice Boltzmann model for the shallow water equations[J]. Comput. Methods Appl. Mech. Engrg., 2002, 191: 3527–3539.

    Article  MathSciNet  Google Scholar 

  14. BEHREND O. Solid boundaries in particle suspension simulations via lattice Boltzmann method[J]. Phys. Rev. E, 1995, 52: 1164–1175.

    Article  Google Scholar 

  15. HE X. Y., ZOU Q. S., LUO L. S. et al. Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model[J]. J. Stat. Phys., 1997, 87: 115–136.

    Article  MathSciNet  Google Scholar 

  16. ZOU QI-SU, HE XIAO-yI. On perssure and velocity boundary conditions for the Lattice Boltzmann BGK model[J]. Phys. Fluids, 1997, 9: 1591–1598.

    Article  MathSciNet  Google Scholar 

  17. MEI R. W., LUO L. S. and SHYY W. An accurate curved boundary treatment in the lattice Boltzmann method[J]. J. Comput. Phys., 1999, 155: 307–330.

    Article  Google Scholar 

  18. FILIPPOVA O., HÄNEL D. Grid refinement for lattice-BGK models[J]. Journal of Comput. Phys., 1998, 147: 219–228.

    Article  Google Scholar 

  19. WANG XING-yONG, SUO LI-sHENG, and LIU DE-yOU. Lattice Boltzmann method with double meshes [J]. J. Hydrodynamics, Ser. B, 2003, 15 (1): 90–96.

    Google Scholar 

  20. WANG JI-wEN, LIU RU-xUN. A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems[J]. Math. Comput. Simulation, 2000, 53: 171–184.

    Article  MathSciNet  Google Scholar 

  21. LI HONG, LIU RU-xUN, The discontinuous Galerkin finite element method for the 2D shallow water equations[J], Math. Comput. Simulation, 2001, 56: 223–233.

    Article  MathSciNet  Google Scholar 

  22. WANG JIA-sONG., NI Han-gen and JIN Sheng. Simulation of propagation, reflection and diffraction of bores caused by sudden and full destruction of a dam[J]. Journal of Hydrodynamics, Ser. A, 2000, 15 (1): 1–7 (in Chinese).

    Google Scholar 

  23. WANG JIA-sONG, HE YOU-sHENG. High resolution numerical model for shallow water flows and pollutant diffusions[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23: 741–747.

    Article  Google Scholar 

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Correspondence to Ya-li Duan.

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Project supported by the National Natural Science Foundation of China (Grant Nos. 10371118, 90411009).

Biography: DUAN Ya-li (1973), Female, Ph. D., Lecturer

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Duan, Yl., Liu, Rx. Lattice Boltzmann Simulations of Triagular Cavity Flow and Free-Surface Problems. J Hydrodyn 19, 127–134 (2007). https://doi.org/10.1016/S1001-6058(07)60038-9

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  • DOI: https://doi.org/10.1016/S1001-6058(07)60038-9

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