×

A new explicit immersed boundary method for simulation of fluid-solid interactions. (English) Zbl 1488.35422

Summary: A new Explicit Immersed Boundary method (IBM) is presented in this work by analyzing and simplifying the system of equations developed from the implicit boundary condition-enforced immersed boundary method. By this way, the requirement to solve the matrix system has been bypassed. It makes the solver be computationally less expensive, especially when large number of Lagrangian points are used to represent the solid boundary. The lattice Boltzmann Flux solver (LBFS) was chosen as the flow solver in this paper as it combines the advantages of both Lattice Boltzmann (LB) solver and Navier- Stokes solver. However, it should be indicated that the new IBM can be incorporated into any flow solver. Comprehensive validations demonstrate that the new explicit scheme bears comparable numerical accuracy as the previous implicit IBM when having a geometry with curvature. The new method is computationally much more efficient than the previous method, especially for moving boundary problems.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids

Software:

Proteus
Full Text: DOI

References:

[1] R. GLOWINSKI, T.-W. PAN, T. I. HESLA, AND D. D. JOSEPH, A distributed Lagrange multi-plier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, 25 (1999), pp. 755-794. · Zbl 1137.76592
[2] Y. NAKAYAMA, K. KIM, AND R. YAMAMOTO, Simulating (electro) hydrodynamic effects in col-loidal dispersions: smoothed profile method, The European Phys. J. E, 26 (2008), pp. 361-368.
[3] T. YE, R. MITTAL, H. UDAYKUMAR, AND W. SHYY, An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., 156 (1999), pp. 209-240. · Zbl 0957.76043
[4] R. MITTAL AND G. IACCARINO, Immersed boundary methods, Annu. Rev. Fluid Mech., 37 (2005), pp. 239-261. · Zbl 1117.76049
[5] C. S. PESKIN, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220-252. · Zbl 0403.76100
[6] R. P. BEYER AND R. J. LEVEQUE, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal., 29 (1992), pp. 332-364. · Zbl 0762.65052
[7] M.-C. LAI AND C. S. PESKIN, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000), pp. 705-719. · Zbl 0954.76066
[8] C. S. PESKIN, Flow patterns around heart valves: A numerical method, J. Comput. Phys., 10 (1972), pp. 252-271. · Zbl 0244.92002
[9] E. SAIKI AND S. BIRINGEN, Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. Comput. Phys., 123 (1996), pp. 450-465. · Zbl 0848.76052
[10] Z.-G. FENG AND E. E. MICHAELIDES, The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys., 195 (2004), pp. 602-628. · Zbl 1115.76395
[11] Z.-G. FENG AND E. E. MICHAELIDES, Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202 (2005), pp. 20-51. · Zbl 1076.76568
[12] D. GOLDSTEIN, R. HANDLER AND L. SIROVICH, Modeling a no-slip flow boundary with an external force field, J. Comput. Phys., 105 (1993), pp. 354-366. · Zbl 0768.76049
[13] A. DE ROSIS, S. UBERTINI AND F. UBERTINI, A partitioned approach for two-dimensional fluid-structure interaction problems by a coupled lattice Boltzmann-finite element method with im-mersed boundary, J. Fluids Structures, 45 (2014), pp. 202-215.
[14] A. DE ROSIS, S. UBERTINI AND F. UBERTINI, A comparison between the interpolated bounce-back scheme and the immersed boundary method to treat solid boundary conditions for laminar flows in the lattice Boltzmann framework, J. Sci. Comput., 61 (2014), pp. 477-489. · Zbl 1417.76035
[15] K. SUZUKI AND T. INAMURO, Effect of internal mass in the simulation of a moving body by the immersed boundary method, Comput. Fluids, 49 (2011), pp. 173-187. · Zbl 1271.76257
[16] Y. CHEN, Q. CAI, Z. XIA, M. WANG AND S. CHEN, Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions, Phys. Rev. E, 88 (2013), 013303.
[17] X. NIU, C. SHU, Y. CHEW AND Y. PENG, A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A, 354 (2006), pp. 173-182. · Zbl 1181.76111
[18] J. WU AND C. SHU, Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys., 228 (2009), pp. 1963-1979. · Zbl 1243.76081
[19] Y. WANG, C. SHU AND C. TEO, Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows, Comput. Fluids, 94 (2014), pp. 98-111. · Zbl 1391.76446
[20] Z. GUO AND C. SHU, Lattice Boltzmann method and Its Applications in Engineering, World Scientific, 2013. · Zbl 1278.76001
[21] Y. WANG, C. SHU, H. B. HUANG AND C. J. TEO, Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio, J. Comput. Phys., 280 (2015), pp. 404-423. · Zbl 1349.76746
[22] C. SHU, N. LIU AND Y.-T. CHEW, A novel immersed boundary velocity correction-lattice Boltz-mann method and its application to simulate flow past a circular cylinder, J. Comput. Phys., 226 (2007) pp. 1607-1622. · Zbl 1173.76395
[23] Y. WANG, C. SHU, L. YANG AND Y. SUN, On the immersed boundary-lattice Boltzmann simula-tions of incompressible flows with freely moving objects, Int. J. Numer. Methods Fluids, 83 (2017), pp. 331-350.
[24] R. K. SHUKLA, M. TATINENI AND X. ZHONG, Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations, J. Comput. Phys., 224 (2007), pp. 1064-1094. · Zbl 1123.76044
[25] S. DENNIS AND G.-Z. CHANG, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J. Fluid Mech., 42 (1970), pp. 471-489. · Zbl 0193.26202
[26] X. HE AND G. DOOLEN, Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. Comput. Phys., 134 (1997), pp. 306-315. · Zbl 0886.76072
[27] M. BRAZA, P. CHASSAING AND H. H. MINH, Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, J. Fluid Mech., 165 (1986), pp. 79-130. · Zbl 0596.76047
[28] M. BENSON, P. BELLAMY-KNIGHTS, J. GERRARD AND I. GLADWELL, A viscous splitting algorithm applied to low Reynolds number flows round a circular cylinder, J. Fluids Structures, 3 (1989), pp. 439-479. · Zbl 0695.76023
[29] H. DING, C. SHU, K. YEO AND D. XU, Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput. Methods Appl. Mech. Eng., 193 (2004), pp. 727-744. · Zbl 1068.76062
[30] Z. FARUQUEE, D. S. TING, A. FARTAJ, R. M. BARRON AND R. CARRIVEAU, The effects of axis ratio on laminar fluid flow around an elliptical cylinder, Int. J. Heat Fluid Flow, 28 (2007), pp. 1178-1189.
[31] E. GUILMINEAU AND P. QUEUTEY, A numerical simulation of vortex shedding from an oscillating circular cylinder, J. Fluids Structures, 16 (2002), pp. 773-794.
[32] D. WAN AND S. TUREK, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int. J. Numer. Methods Fluids, 51 (2006), pp. 531-566. · Zbl 1145.76406
[33] A. ANDERSEN, U. PESAVENTO AND Z. J. WANG, Unsteady aerodynamics of fluttering and tumbling plates, J. Fluid Mech., 541 (2005). · Zbl 1082.76037
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.