A LATTICE BOLTZMANN APPROACH FOR THREE-DIMENSIONAL TSUNAMI SIMULATION BASED ON THE PLIC-VOF METHOD
AbstractFree surface flow problems occur in numerous disaster simulations, such as tsunamis inland penetration in urban area. Simulation models for these problems have to be non-hydrostatic and three-dimensional because of the strong non-linearity and higher-order physical phenomena. Despite all the progress in the modern computational fluid dynamics, such simulations still present formidable challenges both from numerical and computational cost point of view. The lattice Boltzmann method (LBM) has been attracting attention as an alternative fluid simulation tool to overcome the problems. In current study, LBM for three-dimensional tsunami simulations is developed which are coupled with the piecewise linear interface calculation with the Volume of Fluid (VOF) approach. This model is for an efficient three-dimensional tsunami simulation by a one-fluid formulation, where the lattice Boltzmann equation is assigned to solve for a single virtual fluid. Various benchmark problems are also carried out to validate the utility of the proposed models in term of coastal engineering.
Anderl, D., Bogner, S., Rauh, C., Rude, U., and Delgado, A. Free surface lattice Boltzmann with enhanced bubble model. Comput. Math. with Appl., 67(2):331-339, 2014.
Asai, M., Aly, A. M., Sonoda, Y., and Sakai, Y. A stabilized incompressible SPH method by relaxing the density invariance condition. J. Appl. Math., 2012:1-24, 2012.
Aulisa, E., Manservisi, S., Scardovelli, R., and Zaleski, S. A geometrical area-preserving Volume-of- Fluid advection method. J. Comput. Phys., 192(1):355-364, 2003.
Aulisa, E., Manservisi, S., Scardovelli, R., and Zaleski, S. Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry. J. Comput. Phys., 225(2):2301-2319, 2007.
Bhatnagar, P. L., Gross, E. P., and Krook, M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94(3):511-525, 1954.
Bouzidi, M., Firdaouss, M., and Lallemand, P. Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids, 13(11):3452-3459, 2001.
Chen, H., Chen, S., and Matthaeus, W. H. Recovery of the Navier-Stokes equations using a lattice-gas Soltzmann method. Phys. Rev. A, 45(8):5339-5342, 1992.
Choi, B. H., Kim, D. C., Pelinovsky, E., and Woo, S. B. Three-dimensional simulation of tsunami run-up around conical island. Coast. Eng., 54(8):618-629, 2007.
Grilli, S. T., Skourup, J., and Svendsen, I. A. An efficient boundary element method for nonlinear water waves. Engng. Anal. Bound. Elem., 6(2):97-107, 1989.
Hardy, J., De Pazzis, O., and Pomeau, Y. Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions. Phys. Rev. A, 13(5):1949-1961, 1976.
He, X. and Luo, L. S. Lattice boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys., 88(3/4):927-944, 1997.
Hirt, C. W. and Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39(1):201-225, 1981.
Hu, K. C., Hsiao, S. C., Hwung, H. H., and Wu, T. R. Three-dimensional numerical modeling of the interaction of dam-break waves and porous media. Adv. Water Resour., 47:14-30, 2012.
JanÃŸen, Christian and Krafczyk, Manfred. Free surface flow simulations on GPGPUs using the LBM. Comput. Math. with Appl., 61(12):3549-3563, 2011.
Khayyer, A. and Gotoh, H. Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure. Coast. Eng., 56(4):419-440, 2009.
Kleefsman, K. M. T., Fekken, G., Veldman, A. E. P., Iwanowski, B., and Buchner, B. A Volumeof- Fluid based simulation method for wave impact problems. J. Comput. Phys., 206(1):363-393, 2005.
Kölke, A. Modellierung und diskretisierung bewegter diskontinuitäten in randgekoppelten Mehrfeldsystemen. PhD thesis, Technische Universität Braunschweig, 2005.
Körner, C., Thies, M., Hofmann, T., Thurey, N., and Rude, U. Lattice Boltzmann model for free surface flow for modeling foaming. J. Stat. Phys., 121(1-2):179-196, 2005.
Koshizuka, S. and Oka, Y. Moving-Particle Semi-implicit method for fragmentation of incompressible fluid. Nucl. Sci. Eng., 123:421-434, 1996.
Kunugi, T. and Kino, C. DNS of falling film structure and heat transfer via MARS method. Comput. Struct., 83(6-7):455-462, 2005.
Longuet-Higgins, M. S. and Cokelet, E. D. The deformation of steep surface waves on water: a numerical method of computation. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 350, pages 1-26. The Royal Society, 1976.
Lubin, P., Vincent, S., Abadie, S., and Caltagirone, J. P. Three-dimensional Large Eddy Simulation of air entrainment under plunging breaking waves. Coast. Eng., 53(8):631-655, 2006.
Maier, R. S., Bernard, R. S., and Grunau, D.W. Boundary conditions for the lattice Boltzmann method. Phys. Fluids, 8(7):1788-1801, 1996.
Martin, J. C. and Moyce, W. J. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos. Trans. R. Soc. A Math. Phys. Eng., 244:312-324, 1952.
McNamara, G. R. and Zanetti, G. Use of the boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett., 61(20):2332-2335, 1988.
Nichols, B D and Hirt, C W. Improved free surface conditions for numerical incompressible flow computations. J. Comput. Phys., 8:434-448, 1971. ISSN 00219991.
Nishi, Y. and Doan, P. V. Hybrid boundary condition combined with data assimilation for simulations of free surface flows using lattice Boltzmann method. Comput. Fluids, 88:108-114, 2013.
Noh, W. F. and Woodward, P. SLIC (simple line interface calculation). In Proceedings, Fifth International Conference on Fluid Dynamics, volume 59, pages 330-340, Berlin, 1976. Springer.
Obrecht, C., Kuznik, F., Tourancheau, B., and Roux, J. J. A new approach to the lattice Boltzmann method for graphics processing units. Comput. Math. with Appl., 61(12):3628-3638, 2011.
Obrecht, C., Kuznik, F., Tourancheau, B., and Roux, J. J. Scalable lattice Boltzmann solvers for CUDA GPU clusters. Parallel Comput., 39(6-7):259-270, 2013.
Onodera, N. and Idomura, Y. Acceleration of wind simulation using locally mesh-refined lattice boltzmann method on gpu-rich supercomputers. In Supercomputing Frontiers, pages 128-145, Cham, 2018. Springer International Publishing.
Pilliod, J. E. and Puckett, E. G. Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys., 199(2):465-502, 2004.
Qian, Y. H., D'Humières, D., and Lallemand, P. Lattice BGK models for Navier-Stokes Equation. Europhys. Lett., 6(17):479-484, 1992.
Rinaldi, P. R., Dari, E. A., Vénere, M. J., and Clausse, A. A Lattice-Boltzmann solver for 3D fluid simulation on GPU. Simul. Model. Pract. Theory, 25:163-171, 2012.
Rudman, M. Volume-tracking methods for interfacial flow calculations. Int. J. Numer. Methods Fluids, 24:671-691, 1997.
Safi, M. A. and Turek, S. GPGPU-based rising bubble simulations using a MRT lattice Boltzmann method coupled with level set interface capturing. Comput. Fluids, 124:170-184, 2016.
Scardovelli, R. and Zaleski, S. Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J. Comput. Phys., 164(1):228-237, 2000.
Shigeto, Y. and Sakai, M. Arbitrary-shaped wall boundary modeling based on signed distance functions for granular flow simulations. Chem. Eng. J., 231:464-476, 2013.
Succi, S., Foti, E., and Higuera, F. Three-dimensional flows in complex geometries with the lattice Boltzmann method. Europhys. Lett., 10(5):433-438, 1989.
Sun, X. and Sakai, M. Three-dimensional simulation of gas-solid-liquid flows using the DEM-VOF method. Chem. Eng. Sci., 134:531-548, 2015.
Sun, Z., Djidjeli, K., Xing, J. T., and Cheng, F. Modified MPS method for the 2D fluid structure interaction problem with free surface. Comput. Fluids, 122(February):47-65, 2015.
Thurey, N. and Rude, U. Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids. Comput. Vis. Sci., 12(5):247-263, 2009.
Wroniszewski, P. A., Verschaeve, J. C. G., and Pedersen, G. K. Benchmarking of Navier-Stokes codes for free surface simulations by means of a solitary wave. Coast. Eng., 91:1-17, 2014.
Wu, Y. T., Yeh, C. L., and Hsiao, S. C. Three-dimensional numerical simulation on the interaction of solitary waves and porous breakwaters. Coast. Eng., 85:12-29, 2014.
Youngs, D. Time-dependent multi-material flow with large fluid distortion. Numer. Methods Fluid Dyn., (October):273-285, 1982.
Zabelok, S., Arslanbekov, R., and Kolobov, V. Adaptive kinetic-fluid solvers for heterogeneous computing architectures. J. Comput. Phys., 303:455-469, 2015.