## Regularized characteristic boundary conditions for the lattice-Boltzmann methods at high Reynolds number flows.(English)Zbl 1378.76097

Summary: This paper reports the investigations done to adapt the characteristic boundary conditions (CBC) to the lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then, all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number ($$Re = 10^5$$), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (finite difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.

### MSC:

 76M28 Particle methods and lattice-gas methods 76N15 Gas dynamics (general theory) 76M20 Finite difference methods applied to problems in fluid mechanics

Palabos
Full Text:

### References:

 [1] Tucker, P. G.; Debonis, J. R.: Aerodynamics, computers and the environment. Philos. trans. R. soc., math. Phys. eng. Sci. 372, No. 2022 (2014) [2] Chen, S.; Doolen, G. D.: Lattice Boltzmann method for fluid flows. Annu. rev. Fluid mech. 30, No. 1, 329-364 (1998) · Zbl 1398.76180 [3] Succi, S.: The lattice Boltzmann equation: for fluid dynamics and beyond. Numer. math. Sci. comput. (2001) · Zbl 0990.76001 [4] Lallemand, P.; Luo, L. -S.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. rev. E 61, 6546-6562 (2000) [5] Buick, J. M.; Greated, C. A.; Campbell, D. M.: Lattice BGK simulation of sound waves. Europhys. lett. 43, No. 3, 235 (1998) · Zbl 1185.76828 [6] Marié, S.; Ricot, D.; Sagaut, P.: Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics. J. comput. Phys. 228, No. 4, 1056-1070 (2009) · Zbl 1330.76115 [7] Heuveline, V.; Krause, M. J.; Latt, J.: Towards a hybrid parallelization of lattice Boltzmann methods. Comput. math. Appl. 58, No. 5, 1071-1080 (2009) · Zbl 1189.76408 [8] Colonius, T.: Modeling artificial boundary conditions for compressible flow. Annu. rev. Fluid mech. 36, No. 1, 315-345 (2004) · Zbl 1076.76040 [9] Bodony, D. J.: Analysis of sponge zones for computational fluid mechanics. J. comput. Phys. 212, No. 2, 681-702 (2006) · Zbl 1161.76539 [10] Israeli, M.; Orszag, S. A.: Approximation of radiation boundary conditions. J. comput. Phys. 41, No. 1, 115-135 (1981) · Zbl 0469.65082 [11] Poinsot, T.; Lele, S.: Boundary conditions for direct simulations of compressible viscous flows. J. comput. Phys. 101, No. 1, 104-129 (1992) · Zbl 0766.76084 [12] Yoo, C. S.; Wang, Y.; Trouvé, A.; Im, H. G.: Characteristic boundary conditions for direct simulations of turbulent counterflow flames. Combust. theory model. 9, No. 4, 617-646 (2005) · Zbl 1086.80006 [13] Lodato, G.; Domingo, P.; Vervisch, L.: Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows. J. comput. Phys. 227, No. 10, 5105-5143 (2008) · Zbl 1388.76098 [14] Izquierdo, S.; Fueyo, N.: Characteristic nonreflecting boundary conditions for open boundaries in lattice Boltzmann methods. Phys. rev. E 78 (2008) · Zbl 1388.76296 [15] Ginzburg, I.; Verhaeghe, F.; D’humieres, D.: Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions. Commun. comput. Phys. 3, 427-478 (2008) [16] D’humieres, D.: Generalized lattice-Boltzmann equations. Prog. astronaut. Aeronaut. 159, 450-458 (1992) [17] Jung, N.; Seo, H. W.; Yoo, C. S.: Two-dimensional characteristic boundary conditions for open boundaries in the lattice Boltzmann methods. J. comput. Phys. 302, 191-199 (August 2015) · Zbl 1349.76697 [18] Heubes, D.; Bartel, A.; Ehrhardt, M.: Characteristic boundary conditions in the lattice Boltzmann method for fluid and gas dynamics. J. comput. Appl. math. 262, 51-61 (2014) · Zbl 1301.76061 [19] Schlaffer, M. B.: Non-reflecting boundary conditions for the lattice Boltzmann method. (2013) [20] Zou, Q.; He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. fluids 9, No. 6, 1591-1598 (1997) · Zbl 1185.76873 [21] Latt, J.; Chopard, B.; Malaspinas, O.; Deville, M.; Michler, A.: Straight velocity boundaries in the lattice Boltzmann method. Phys. rev. E 77 (2008) [22] Latt, J.; Chopard, B.: Lattice Boltzmann method with regularized pre-collision distribution functions. Math. comput. Simul. 72, No. 2-6, 165-168 (2006) · Zbl 1102.76056 [23] Malaspinas, O.: Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization. (2015) [24] Bhatnagar, P. L.; Gross, E. P.; Krook, M.: A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems. Phys. rev. 94, 511-525 (1954) · Zbl 0055.23609 [25] Qian, Y. H.; D’humières, D.; Lallemand, P.: Lattice BGK models for Navier-Stokes equation. Europhys. lett. 17, No. 6, 479 (1992) · Zbl 1116.76419 [26] Chapman, S.; Cowling, T.: The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases, vol. 2. (1952) · Zbl 0726.76084 [27] Malaspinas, O.; Chopard, B.; Latt, J.: General regularized boundary condition for multi-speed lattice Boltzmann models. Comput. fluids 49, No. 1, 29-35 (2011) · Zbl 1271.76267 [28] Yoo, C. S.; Im, H. G.: Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reaction effects. Combust. theory model. 11, No. 2, 259-286 (2007) · Zbl 1121.80342 [29] Albin, E.; D’angelo, Y.; Vervisch, L.: Flow streamline based Navier-Stokes characteristic boundary conditions: modeling for transverse and corner outflows. Comput. fluids 51, No. 1, 115-126 (2011) · Zbl 1271.76289 [30] Philippi, P. C.; Hegele, L. A.; Dos Santos, L. O. E.; Surmas, R.: From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models. Phys. rev. E 73, No. 5 (2006) [31] Lamb, H.: Hydrodynamics. (1932) · Zbl 0828.01012 [32] Guo, Z.; Zheng, C.; Shi, B.; Zhao, T. S.: Thermal lattice Boltzmann equation for low Mach number flows: decoupling model. Phys. rev. E 75, No. 3 (2007) [33] Yoo, C. S.; Im, H. G.: Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reaction effects. Combust. theory model. 11, No. 2, 259-286 (2007) · Zbl 1121.80342
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.