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 JAMP  Vol.4 No.7 , July 2016
Spectral Element Simulation of Rotating Particle in Viscous Flow
Abstract:

Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the discretization errors in SEM could be reduced exponentially to machine zero so that the spectral convergence rate can be achieved. Inherited the advantage of FEM, SEM can enhance resolution via both h-type and p-type mesh-refinement. A penalty method was utilized to compute force fields in particulate flows involving freely moving rigid particles. Results were analyzed and comparisons were made; therefore, this penalty-implemented SEM was proven to be a viable method for two-phase flow problems.

Cite this paper: Liu, D. and Zhang, N. (2016) Spectral Element Simulation of Rotating Particle in Viscous Flow. Journal of Applied Mathematics and Physics, 4, 1260-1268. doi: 10.4236/jamp.2016.47132.
References

[1]   Mand?, M., Yin, C., S?rensen, H. and Rosendahl, L. (2007) On the Modeling of Motion of Non-Spherical Particles in Two-Phase Flow. 6th International Conference on Multiphase Flow, ICMF 2007, S2_Mon_D_10, Leipzig, 9-13 July 2007.

[2]   Glowinski, R., Pan, T.W., Hesla, T.I. and Joseph, D.D. (1999) A Distributed Lagrangian Multiplier Fictitious Domain Method for Particulate Flow. International Journal of Multiphase Flow, 25, 775-794. http://dx.doi.org/10.1016/S0301-9322(98)00048-2

[3]   Joseph, D.D. and Ocando, D. (2002) Slip Velocity and Lift. Journal of Fluid Mechanics, 454, 263-286. http://dx.doi.org/10.1017/S0022112001007145

[4]   Johnson, A. and Tezduyar, T.E. (1997) 3D Simulation of Fluid-Particle Interactions with the Number of Particles Reaching 100. Computer Methods in Applied Mechanics and Engineering, 145, 301-321. http://dx.doi.org/10.1016/S0045-7825(96)01223-6

[5]   Maxey, M.R., Patel, B.K., Chang, E.J. and Wang, L.-P. (1997) Simulations of Dispersed Turbulent Multiphase Flow. Fluid Dynamics Research, 20, 143-156. http://dx.doi.org/10.1016/S0169-5983(96)00042-1

[6]   Hu, H., Patankar, N. and Zhu, M. (2001) Direct Numerical Simulations of Fluid-Solid Systems Using The Arbitrary Lagrangian-Eulerian Technique. Journal of Computational Physics, 169, 427-462. http://dx.doi.org/10.1006/jcph.2000.6592

[7]   Liu, D., Maxey, M.R. and Karniadakis, G.E. (2002) A Fast Method For Particulate Microflows. Journal of Microelectromechanical Systems, 11, 691-702. http://dx.doi.org/10.1109/JMEMS.2002.805209

[8]   Markauskas, D., (2006) Discrete Element Modeling of Complex Axisymmetric Particle Flow. Mechanika, 6, 32-38.

[9]   Amsden, A.A. and Hirt, C.W. (1973) YAQUI: An Arbitrary Lagrangian-Eulerian Computer Program for Fluid Flows at All Speeds. Report LA-5100, Los Alamos Scientific Laboratory, Los Alamos.

[10]   Hirt, C.W., Amsden, A.A. and Cook, J.L. (1997) An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds. Journal of Computational Physics, 135, 203-216. http://dx.doi.org/10.1006/jcph.1997.5702

[11]   Apte, S., Martin, M. and Patankar, N.A. (2009) A Numerical Method for Fully Resolved Simulation (FRS) of Rigid Particle-Flow Interactions in Complex Flow. Journal of Computational Physics, 228, 2712-2738. http://dx.doi.org/10.1016/j.jcp.2008.11.034

[12]   Bush, J.W.M., Stone, H.A. and Tanzosh, J.P. (1994) Particle Motion in Rotating Viscous Fluids: Historical Survey and Recent Developments. Current Topics in the Physics of Fluids, 1, 337-344.

[13]   Tanzosh, J.P. and Stone, H.A. (1994) Motion of a Rigid Particle in a Rotating Viscous Fluid: An Integral Equation Approach. Journal of Fluid Mechanics, 275, 225-256. http://dx.doi.org/10.1017/S002211209400234X

[14]   Hynes, J.T., Kapral, R. and Weinberg, M. (1977) Particle Rotation and Translation in a Fluid With Spin. Physica A: Statistical Mechanics and Its Applications, 3, 427-452.

[15]   Bluemink, J.J., Lohse, D., Prosperetti, A. and Wijngaarden, V. (2010) Drag and Lift Forces on Particles in a Rotating Flow. Journal of Fluid Mechanics, 643, 1-31. http://dx.doi.org/10.1017/S0022112009991881

[16]   Liu, Q. and Prosperetti, A. (2010) Wall Effects on a Rotating Shere. Journal of Fluid Mechanics, 657, 1-21. http://dx.doi.org/10.1017/S002211201000128X

[17]   Lee, J. and Ladd, A.J.C. (2007) Particle Dynamics and Pattern Formation in a Rotating Suspension. Journal of Fluid Mechanics, 577, 183-209. http://dx.doi.org/10.1017/S002211200700465X

[18]   Liu, D., Keaveny, E., Maxey, M. and Karniadakis, G.E. (2009) Force Coupling Method for Flows with Ellipsoidal Particles. Journal of Computational Physics, 228, 3559-3581. http://dx.doi.org/10.1016/j.jcp.2009.01.020

[19]   Liu, D., Chen, Q. and Wang, Y. (2011) Spectral Element Modeling of Sediment Transport in Shear Flows. Computer Methods in Applied Mechanics and Engineering, 200, 1691-1707. http://dx.doi.org/10.1016/j.cma.2011.01.009

[20]   Liu, D., Zheng, Y.-L. and Chen, Q. (2015) Grain-Resolved Simulation of Micro-Particle Dynamics in Shear and Oscillatory Flows. Computers and Fluids, 108, 129-141. http://dx.doi.org/10.1016/j.compfluid.2014.12.003

[21]   Kim, S. and Karrila, S.J. (1991) Microhydrodynamics: Principles and Selected Applications. Dover Publications, Inc., Mineola, New York.

[22]   Liu, D. (2004) Spectral Element/Force Coupling Method: Application to Colloidal Micro-Devices and Self-Assembled Particles Structures in 3D Domains. Ph.D. Dissertation, Brown University, Providence.

[23]   Warburton, T.C., Sherwin, S.J. and Karniadakis, G.E. (1999) Spectral Basis Functions for 2D Hybrid hp Elements. SIAM Journal on Scientific Computation, 20, 1671-1695. http://dx.doi.org/10.1137/S1064827597315716

[24]   Karniadakis, G.E. and Sherwin, S.J. (2005) Spectral/hp Element Methods for CFD. Oxford University Press, Oxford. http://dx.doi.org/10.1093/acprof:oso/9780198528692.001.0001

[25]   Dance, S. (2002) Particle Sedimentation in Viscous Fluids. Ph.D. Dissertation, Brown University, Providence.

 
 
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