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An improved immersed boundary method with direct forcing for the simulation of particle laden flows. (English) Zbl 1402.76143
Summary: An efficient approach for the simulation of finite-size particles with interface resolution was presented by M. Uhlmann [J. Comput. Phys. 209, No. 2, 448–476 (2005; Zbl 1138.76398)]. The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling yielding a substantially better imposition of boundary conditions at the interface, even for large time steps. Furthermore, it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1, hence excluding, for example, non-buoyant particles. This can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0.3. This paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size. A remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner. The resulting algorithm is thoroughly validated and is demonstrated to substantially improve upon the original method.

MSC:
76T20 Suspensions
Software:
IIMPACK; hypre
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[1] Apte, S.V.; Martin, M.; Patankar, N.A., A numerical method for fully resolved simulation (FRS) of rigid particle-flow interactions in complex flows, J. comput. phys., 228, 2712-2738, (2009) · Zbl 1282.76148
[2] Bagchi, P.; Balachandar, S., Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate re, Phys. fluids, 14, 2719-2737, (2002) · Zbl 1185.76040
[3] W.P. Breugem, M. Poriquie, B.J. Boersma, Some issues related to the stress IB method for flow around obstacles. in: Proceedings of the Academy colloquium: Immersed Bounday Methods: Current status and future research direction, Amsterdam, The Netherlands, 15-17 June 2009.
[4] Cheny, Y.; Botella, O., The LS-STAG method: a new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties, J. comput. phys., 229, 1043-1076, (2010) · Zbl 1329.76252
[5] Chow, E.; Cleary, A.J.; Falgout, R.D., Design of the hypre preconditioner library, (), 106-116
[6] R.D. Falgout, U.M. Yang, hypre: a library of high performance preconditioners, in: International Conference on Computational Science, vol. 3, 2002, pp. 632-641. · Zbl 1056.65046
[7] Ferzinger, J.H.; Peric, M., Computational methods for fluid dynamics, (2002), Springer-Verlag
[8] Francois, M.; Uzgoren, E.; Jackson, J.; Shyy, W., Multigrid computations with the immersed boundary technique for multiphase flows, Int. J. numer. methods heat fluid flow, 14, 98-115, (2004) · Zbl 1064.76081
[9] Gilmanov, A.; Sotiropoulos, F., A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies, J. comput. phys., 207, 457-492, (2005) · Zbl 1213.76135
[10] Glowinski, R.; Pan, T.W.; Hesla, T.I.; Joseph, D.D.; Priaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J. comput. phys., 169, 363-426, (2001) · Zbl 1047.76097
[11] Glowinski, R.; Pan, T.-W.; Hesla, T.I.; Joseph, D.D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. multiphase flow, 25, 755-794, (1999) · Zbl 1137.76592
[12] Harlow, F.H.; Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. fluids, 8, 2182-2189, (1965) · Zbl 1180.76043
[13] Iaccarino, G.; Verzicco, R., Immersed boundary technique for turbulent flow simulations, Appl. mech. rev., 56, 331-347, (2003)
[14] T. Kempe, J. Fröhlich, Collision modeling for the interface-resolved simulation of spherical particles in viscous fluids, submitted for publication. · Zbl 1275.76206
[15] Kim, D.; Choi, H., Immersed boundary method for flow around an arbitrarily moving body, J. comput. phys., 212, 662-680, (2006) · Zbl 1161.76520
[16] Le, D.V.; Khoo, B.C.; Lim, K.M., An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Comput. methods appl. mech. eng., 197, 25-28, 2119-2130, (2008) · Zbl 1158.76407
[17] Leopardi, P., A partition of the unit sphere into regions of equal area and small diameter, Electron. trans. numer. anal., 25, 309-327, (2006) · Zbl 1160.51304
[18] Li, Z.; Ito, K., The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains, Soc. indus. math., (2006)
[19] Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A., A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. comput. phys., 227, 4825-4852, (2008) · Zbl 1388.76263
[20] Mittal, R.; Iaccarino, G., Immersed boundary methods, Ann. rev. fluid mech., 37, 239-261, (2005) · Zbl 1117.76049
[21] J. Mohd-Yusof, Combined immersed boundary/B-Spline method for simulations of flows in complex geometries, Center for Turbulence Research, Annual Research Briefs, NASA Ames/ Stanford University, pp. 317-327, 1997.
[22] Mordant, N.; Pinton, J.-F., Velocity measurement of a settling sphere, Eur. phys. J. B, 18, 343-352, (2000)
[23] Nirschl, H.; Dwyer, H.A.; Denk, V., Three-dimensional calculations of the simple shear flow around a single particle between two moving walls, J. fluid mech., 283, 273-285, (1995) · Zbl 0839.76019
[24] Oevermann, M.; Scharfenberg, C.; Klein, R., A sharp interface finite volume method for elliptic equations on Cartesian grids, J. comput. phys., 228, 5184-5206, (2009) · Zbl 1169.65343
[25] Pan, T.-W.; Glowinski, R., Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow, J. comput. phys., 181, 260-279, (2002) · Zbl 1178.76235
[26] Peskin, Ch. S., Numerical analysis of blood flow in the heart, J. comput. phys., 25, 220-252, (1977) · Zbl 0403.76100
[27] Peskin, Ch. S., The immersed boundary method, Acta numer., 11, 479-517, (2003) · Zbl 1123.74309
[28] Prosperetti, A.; Tryggvason, G., Computational methods for multiphase flow, (2007), Cambridge University Press
[29] Roma, A.M.; Peskin, Ch. S.; Berger, M.J., An adaptive version of the immersed boundary method, J. comput. phys., 153, 509-534, (1999) · Zbl 0953.76069
[30] Roman, F.; Armenio, V.; Fröhlich, J., A simple wall-layer model for large eddy simulation with immersed boundary method, Phys. fluids, 21, 101701, (2009) · Zbl 1183.76440
[31] Roman, F.; Napoli, E.; Milici, B.; Armenio, V., An improved immersed boundary method for curvilinear grids, Comput. fluids, 38, 1510, (2009) · Zbl 1242.76210
[32] Sharma, N.; Patankar, N.A., A fast computation technique for the direct numerical simulation of rigid particulate flows, J. comput. phys., 205, 439-457, (2005) · Zbl 1087.76533
[33] Spalart, P.R.; Moser, R.D.; Rogers, M.M., Spectral methods for the navier – stokes equations with one infinite and two periodic directions, J. comput. phys., 96, 297-324, (1991) · Zbl 0726.76074
[34] T. Stoesser, J. Fröhlich, W. Rodi, Turbulent open channel flow over a permeable bed, in: 32th IAHR Congress, Venice, Italy, July 1-6, 2007.
[35] ten Cate, A.; Nieuwstad, C.H.; Derksen, J.J.; Van den Akker, H.E.A., Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. fluids, 14, 4012-4025, (2002) · Zbl 1185.76073
[36] Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y.-J., A front-tracking method for the computations of multiphase flow, J. comput. phys., 169, 708-759, (2001) · Zbl 1047.76574
[37] G. Tryggvason, S. Thomas, J. Lu, B. Aboulhasanzadeh, V. Tsengue, Multiscale computation of multiphase flows, in: 7th International Conference on Multiphase Flows, Tampa, Florida, USA, 2010. · Zbl 1228.76183
[38] Udaykumar, H.S.; Kan, H.-C.; Shyy, W.; Tran-Son-Tay, R., Multiphase dynamics in arbitrary geometries on fixed Cartesian grids, J. comput. phys., 137, 366-405, (1997) · Zbl 0898.76087
[39] Udaykumar, H.S.; Mittal, R.; Rampunggoon, P.; Khanna, A., A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, J. comput. phys., 174, 345-380, (2001) · Zbl 1106.76428
[40] M. Uhlmann. First experiments with the simulation of particulate flows, Technical Report No. 1020, CIEMAT, Madrid, Spain, 2003, ISSN pp. 1135-9420.
[41] M. Uhlmann. New results on the simulation of particulate flows, Technical Report No. 1038, CIEMAT, Madrid, Spain, 2003, ISSN, pp. 1135-9420.
[42] Uhlmann, M., An immersed boundary method with direct forcing for the simulation of particulate flows, J. comput. phys., 209, 448-476, (2005) · Zbl 1138.76398
[43] M. Uhlmann, An improved fluid-solid coupling method for DNS of particulate flow on a fixed mesh, in M. Sommerfeld, (Ed.,) Proc. 11th Workshop Two-Phase Flow Predictions, Merseburg, Germany, 2005, Universität Halle.
[44] Uhlmann, M., Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime, Phys. fluids, 20, 053305, (2008) · Zbl 1182.76785
[45] M. Uhlmann, Private communication, 2010.
[46] Unverdi, S.O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows, J. comput. phys., 100, 25-37, (1992) · Zbl 0758.76047
[47] Uzgoren, E.; Singh, R.; Sim, J.; Shyy, W., Computational modeling for multiphase flows with spacecraft application, Prog. aerosp. sci., 43, 138-192, (2007)
[48] Sint-Annaland van, M.; Deen, N.G.; Kuipers, J.A.M., Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method, Chem. eng. sci., 60, 2999-3011, (2005)
[49] Verzicco, R.; Mohd-Yusof, J.; Orlandi, P.; Haworth, D., LES in complex geometries using boundary body forces, Aiaa j., 38, 427-433, (2000)
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