Abstract
In this paper, a method that combines the characteristic-based split finite element method (CBS-FEM) and the direct forcing immersed boundary (IB) method is proposed for the simulation of incompressible viscous flows. The structured triangular meshes without regarding the location of the physical boundary of the body is adopted to solve the flow, and the no-slip boundary condition is imposed on the interface. In order to improve the computational efficiency, a grid stretching strategy for the background structured triangular meshes is adopted. The obtained results agree very well with the previous numerical and experimental data. The order of the numerical accuracy is shown to be between 1 and 2. Moreover, the accuracy control by adjusting the number density of the mark points purely at certain stages is explored, and a second power law is obtained. The numerical experiments for the flow around a cylinder behind a backward-facing step show that the location of the cylinder can affect the sizes and the shapes of the corner eddy and the main recirculation region. The proposed method can be applied further to the fluid dynamics with complex geometries, moving boundaries, fluid-structure interactions, etc..
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PESKIN C. S. Flow patterns around heart valves: A numerical method[J[. Journal of Computational Physics, 1972, 10(2): 252–271.
STERN F., WANG Z. and YANG J. et al. Recent progress in CFD for naval architecture and ocean engineering[J]. Journal of Hydrodynamics, 2015, 27(1): 1–23.
SHAO J. Y., SHU C. and CHEW Y. T. Development of an immersed boundary-phase field-lattice Boltzmann method for Neumann boundary condition to study contact line dynamics[J]. Journal of Computational Physics, 2013, 234: 8–32.
PESKIN C. S. The immersed boundary method[J]. Acta Numerica, 2002, 11: 479–517.
MULEN R. The immersed boundary method for the (2D) incompressible Naiver-Stokes equations[D]. Master Thesis, Delft, The Netherlands: Delft University of Technology, 2006.
MITTAL R., IACCARINO G. Immersed boundary methods[J]. Annual Review of Fluid Mechanics, 2005, 37: 239–261.
LAI M. C., PESKIN C. S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity[J]. Journal of Computational Physics, 2000, 160(2): 705–719.
FADLUN E. A., VERZICCO R. and ORLANDI P. et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics, 2001, 161(1): 30–60.
ZIENKIEWICZ O. C., TAYLOR R. L. and NITHIARASU P. The finite element method, Vol. 3: Fluid dynamics[M]. 6th Edition, Oxford, UK: Butterworth-Heinemann, 2005.
NITHIARASU P. An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows[J]. International Journal for Numerical Methods in Engineering, 2003, 56(13): 1815–1845.
ARPINO F., MASSAROTTI N. and MAURO A. et al. Artificial compressibility based CBS solutions for double diffusive natural convection in cavities[J]. International Journal of Heat and Fluid Flow, 2013, 23(1): 205–225.
NITHIARASU P. An arbitrary Eulerian Lagrangian (ALE) method for free surface flow calculations using the characteristic based split (CBS) scheme[J]. International Journal for Numerical Methods in Fluids, 2005, 48(12): 1415–1428.
SCHLICHTING H. Boundary layer theory[M]. Sixth Edition, New York, USA: McGraw-Hill, 1968.
STRAUSS D., AZEVEDO J. L. F. On the development of an agglomeration multigrid solver for turbulent flows[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2003, 25(4): 315–324.
QU L., NORBERG C. and DAVIDSON L. et al. Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200[J]. Journal of Fluids and Structures, 2013, 39: 347–370.
WU J., SHU C. and ZHANG Y. H. Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-lattice Boltzmann method[J]. International Journal for Numerical Methods in Fluids, 2010, 62(3): 327–354.
SILVA L. E., SILVEIRA-NETO A. and DAMASCENO J. J. R. Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method[J]. Journal of Computational Physics, 2003, 189(2): 351–370.
NIU X. D., SHU C. and CHEW Y. T. et al. A momentum exchanged-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows[J]. Physics Letters A, 2006, 354(3): 173–182.
PENG Y., LUO L. S. A comparative study of immersed-boundary and interpolated bounce-back methods in LBE[J]. Computational Fluid Dynamics, 2008, 8(1): 156–167.
ZHOU Xing-gang, CHEN Xiao-peng and LIU Weiming et al. Two-dimensional simulation of flow around cylinder with multiple-relaxation-time lattice Boltzmann method[J]. Engineering Journal of Wuhan University, 2012, 45(1): 10–15(in Chinese).
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Project supported by the National High Technology Re- search and Development Program of China (863 Program, Grant No. 2012AA011803), the National Natural Scientific Foundation of China (Grant No. 11172241) and the University Foundation for Fundamental Research of NPU (Grant No. JCY-20130121).
Biography: YANG Feng-chao (1989-), Male, Ph. D. Candidate
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Yang, FC., Chen, Xp. Numerical simulation of two-dimensional viscous flows using combined finite element-immersed boundary method. J Hydrodyn 27, 658–667 (2015). https://doi.org/10.1016/S1001-6058(15)60528-5
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DOI: https://doi.org/10.1016/S1001-6058(15)60528-5