Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

doi:10.1007/s10483-017-2290-7

摘要/Abstract

摘要： A method combining the immersed boundary technique and a multirelaxation-time (MRT) lattice Boltzmann flux solver (LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations (LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

关键词: multiple relaxation time, lattice Boltzmann equation (LBE), solid-liquid coupling, multiple nonlinear coupling, moving boundary, liquid storage tank, uplift, time-split-steps, ALE method, incompressible flow, immersed boundary method

Abstract: A method combining the immersed boundary technique and a multirelaxation-time (MRT) lattice Boltzmann flux solver (LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations (LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

Key words: solid-liquid coupling, multiple nonlinear coupling, moving boundary, liquid storage tank, uplift, time-split-steps, ALE method, lattice Boltzmann equation (LBE), multiple relaxation time, immersed boundary method, incompressible flow

中图分类号:

76P05
76D05

Xiaodi WU, Fu CHEN, Huaping LIU. Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(12): 1679-1696.

参考文献

[1] Chen, H., Chen, S., and Matthaeus, H. Recovery of the Navier-Stokes equation using a latticeBoltzmann method. Physical Review A, 45, 5339-5342(1992)
[2] Qian, Y., D'humières, D., and Lallemand, P. Lattice BGK models for Navier-Stokes equations. Europhysics Letters, 17, 479-484(1992)
[3] Shan, X. and Chen, H. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47, 1815-1819(1993)
[4] Suryanarayanan, S., Singh, S., and Ansumali, S. Extended BGK Boltzmann for dense gases. Communications in Computational Physics, 13, 629-648(2013)
[5] Yu, D., Mei, R., Luo, L., and Shyy, W. Various flow computations with the method of lattice Boltzmann equation. Progress in Aerospace Sciences, 39, 329-367(2003)
[6] Aidun, C. and Clausen, J. Lattice Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 42, 439-472(2010)
[7] Yu, H., Girimaji, S. S., and Luo, L. S. DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method. Journal of Computational Physics, 209, 599-616(2005)
[8] Shu, C., Peng, Y., and Zhou, C. F. Application of Taylor series expansion and least-squares-based lattice Boltzmann method to simulate turbulent flows. Journal of Turbulence, 7(37), 1-12(2006)
[9] Li, K., Zhong, C. W., Zhuo, C. S., and Jun, C. Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method. Computational Physics, 204, 265-291(2005)
[10] Shu, C., Wang, Y., Teo, C. J., and Wu, J. Development of lattice Boltzmann flux solver for simulation of incompressible flows. Advances in Applied Mathematics and Mechanics, 6, 436-460(2014)
[11] Wang, Y., Shu, C., and Teo, C. J. Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows. Computers and Fluids, 94, 98-111(2014)
[12] Cao, Y. H. Variable property-based lattice Boltzmann flux solver for thermal flows in the low Mach number limit. International Journal of Heat and Mass Transfer, 103, 254-264(2016)
[13] Wang, Y., Shu, C., Huang, H. B., and Teo, C. J. Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio. Journal of Computational Physics, 280, 404-423(2015)
[14] Lallemand, P. and Luo, L. S. Theory of the lattice Boltzmann method:dispersion, dissipation, isotropy, Galilean invariance and stability. Physical Review E, 61(6), 6546-6562(2002)
[15] D'Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L. S. Multiple-relaxationtime lattice Boltzmann models in three dimensions. Philosophical Transactions of the Royal Society, Mathematical, Physical, and Engineering sciences, 360, 437-451(2002)
[16] Guo, X. X., Zhong, C. W., Zhuo, C. S., and Jun, C. Multiple-relaxation-time lattice Boltzmann method for study of two-lid-driven cavity flow solution multiplicity. Theoretical and Computational Fluid Dynamics, 28, 215-231(2004)
[17] Yu, H. D., Luo, L. S., and Girimaji, S. S. LES of turbulent square jet flow using an MRT lattice Boltzmann model. Computers and Fluids, 35, 957-965(2006)
[18] Nie, D. M., Lin, J. Z., and Qiu, L. M. Direct numerical simulations of the decaying turbulence in rotating flows via the MRT lattice Boltzmann method. International Journal of Computational Fluid Dynamics Dynamics, 27(3), 173-183(2013)
[19] Geller, S., Uphoff, S., and Krafczyk, M. Turbulent jet computations based on MRT and cascaded lattice Boltzmann models. Computers and Mathematics with Applications, 65, 1956-1966(2013)
[20] Mittal, R. and Iaccarino, G. Immersed boundary methods. Annual Review of Fluid Mechanics, 37, 239-261(2005)
[21] Peskin, C. Flow patterns around heart valves:a numerical method. Journal of Computational Physics, 10, 220-252(1972)
[22] Fadlun, E., Verzicco, R., Orlandi, P., and Mohd-Yusof, J. Combined immersed-boundary/finite difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161, 35-60(2000)
[23] Wu, J. and Shu, C., Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. Journal of Computational Physics, 228, 1963-1979(2009)
[24] Wu, J. and Shu, C. An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows. Journal of Computational Physics, 229, 5022-5042(2010)
[25] Wang, Y., Shu, C., Teo, C. J., and Wu, J. An immersed boundary-lattice Boltzmann flux solver and its applications to fluid-structure interaction problems. Journal of Fluids and Structures, 54, 440-465(2015)
[26] Qiu, Y. L., Shu, C., Wu, J., Sun, Y., Yang, L. M., and Guo, T. Q. A boundary condition-enforced immersed boundary method for compressible viscous flows. Computers and Fluids, 136, 104-113(2016)
[27] Ren, W. W., Shu, C., Wu, J., and Yang, W. M. Boundary condition-enforced immersed boundary method for thermal flow problems with Dirichlet temperature condition and its applications. Computers and Fluids, 57, 40-51(2012)
[28] Shukla, R. K., Tatineni, M., and Zhong, X. Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations. Journal of Computational Physics, 24, 1064-1094(2007)
[29] Yuan, R., Zhong, C., and Zhang, H. An immersed-boundary method based on the gas kinetic BGK scheme for incompressible viscous flow. Journal of Computational Physics, 296, 184-208(2015)
[30] Calhoun, D. A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular region. Journal of Computational Physics, 176, 231-275(2002)
[31] Russell, D. and Wang, Z. J. A Cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow. Journal of Computational Physics, 191, 177-205(2003)
[32] Choi, J. I., Oberoi, R. C., Edwards, J. R., and Rosati, J. A. An immersed boundary method for complex incompressible flows. Journal of Computational Physics, 224, 757-784(2007)
[33] Badr, H. M. Laminar combined convection from a horizontal cylinder-parellel and contra flow regimes. International Journal of Heat and Mass Transfer, 27, 15-27(1984)
[34] Badr, H. M. Mixed convection from a straight isothermal tube of elliptical cross-section. International Journal of Heat and Mass Transfer, 37(15), 2343-2365(1994)
[35] Bhattacharyya, S. and Singh, A. K. Vortex shedding and heat transfer dependence on effective Reynolds number for mixed convection around a cylinder in cross flow. International Journal of Heat and Mass Transfer, 53, 3202-3212(2010)
[36] Chang, K. S. and Sa, J. Y. The effect of buoyancy on vortex shedding in the near wake of a circular cylinder. Journal of Fluid Mechanics, 220, 253-266(1990)
[37] Johnson, S. A., Thompson, M. C., and Hourigan, K. Flow past elliptical cylinders at low Reynolds numbers. 14th Australasian Fluid Mechanics Conference Adelaide University, Adelaide, Australia (2001)
[38] Lockard, D. P., Luo, L. S., Milder, S. D., and Singer, B. A. Evaluation of power flow for aerodynamic applications. Journal of Statistical Physics, 107, 423-478(2002)