Abstract
We present a space-time homogenization procedure for multiscale modeling of solid-liquid mixture. The derived mathematical model enables us to set up two separate governing equations at both macro- and micro-scales. The fluid in the macroscopic governing equation is teated as an equivalent homogeneous medium with average or homogenized viscosity and is regarded as an incompressible Newtonian fluid, whose motion is assumed to be governed by the Navier-Stokes equations. The microscopic equations of motion governing the coupling phenomenon of the fluid and solid particles in a certain local domain and are solved to determine the microscopic flow fields under adequate boundary and loading conditions. Then the macrosopic viscosity is determined as the quantity averaged over the microscopic domain and within a certain time interval. The numerical viscosity measurement (NVM) can be realized by this space-time homogenization procedure. A set of NVMs is presented to demonstrate that the solid-liquid mixture considered in this study possibly exhibits a macroscopic flow characteristics of a special type of non-Newtonian fluids.
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References
Benssousan, A., Lions, J.L., Papanicoulau, G.: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978)
Brooks, A.N., Hughes, T.J.R.: Streamline-upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Meth. Appl. M. 32, 199–259 (1982)
Coussot, P., Piau, J.M.: On the behaviour of fine mud suspentions. Rheol. Acta. 33, 175–184 (1994)
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique. 29(1), 47–65 (1979)
Cundall,P. A., Strack O.D.L.: The distinct element method as a tool for research in granular media. Department of Civil and Mineral Engineering Report, Part 2, University of Minnesota, Minnesota (1979)
Holman, J.P.: Heat Transfer, vol. 207. McGraw-Hill (2002)
Hornung, U.: Homogenization and Porous Media. Springer, New York (1991)
Iwashita, K., Oda, M.: Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. 124(3), 285–292 (1998)
Nakamura, T., Yim, S.C.: A non linear three-dimensional coupled fluid-sediment interaction model for large seabed deformation. J. Offshore. Mech. Arct. Eng. 133, 031103 (2011)
Ontowirjo, B., Mano, A.: A turbulent and suspended sediment transport model for plunging breakers. Coast. Eng. J. 50, 349–367 (2008)
Rouse, H.: Modern conceptions of the mechanics of turbulence. T. Am. Soc. Civil. Eng. 102, 463–543 (1937)
Sanchez-Palencia, E.: Non-homogeneous media and vibration theory. In: Lecture Note in Physics, vol. 127. Springer, Berlin (1980)
Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 146–159 (1994)
Terada, K., Asai, M., Yamagishi, M.: Finite cover method for linear and nonlinear analyses of heterogeneous solids. Int. J. Numer. Meth. Eng. 58(9), 1321–1346 (2003)
Terada, K., Kurumatani, M.: Performance assessment of generalized elements in the finite cover method. Finite Elem. Anal. Des. 41, 111–132 (2004)
Tezduyar, T.E.: Stabilized finite element formulations for incompressible flow computations: Adv. Appl. Mech. 28, 1–44 (1991)
Ushijima, S., Kuroda, N.: Multiphase modeling to predict finite deformations of elastic objects in free surface. In: Fluid Structure Interaction \(V\), vol. 105, pp. 34–45. WIT Press (2009)
Yamashita, K., Sugawara, D., Takahashi, T., Imamura, F., Saito, Y., Imato, Y., Kai, T., Uehara, H., Kato, T., Nakata, K., Saka, R., Nishikawa, A.: Numerical simulations of large-scale sediment transport caused by the 2011 Tohoku earthquake tsunami in Hirota Bay. South. Sanriku Coast. Coastal Eng. J. 58(4), 1640015, 1–28 (2016)
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Nomura, R., Terada, K., Takase, S., Moriguchi, S. (2018). A Method of Numerical Viscosity Measurement for Solid-Liquid Mixture. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_17
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DOI: https://doi.org/10.1007/978-3-319-65463-8_17
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