AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
PDF (4.1 MB)
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Assessment of simplified momentum equations for free surface flows through rigid porous media

Wibke Düsterhöft-Wriggers1( )Antonia Larese2Eugenio Oñate3,4Thomas Rung1
Hamburg University of Technology, Hamburg, Germany
Università degli Studi di Padova, Padova, Italy
International Center for Numerical Methods in Engineering, CIMNE, Barcelona, Spain
Universitat Politécnica de Catalunya, Barcelona, Spain
Show Author Information

Abstract

In many applications, free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight inconsistencies in the formulation of the governing equations can be found in the literature. The main goal of this paper is to identify these differences and provide a quantitative assessment of different approaches. Following a review of the different formulations, simulation results obtained from three alternative formulations are compared with experimental and numerical data. Results obtained by 2D and 3D test cases indicate that the predictive differences returned by the different formulations remain small for most applications, in particular for small porous Reynolds number ReP < 5000. Thus it seems justified to select a simplified formulation that supports an efficient algorithm and coding structure in a computational fluid dynamics environment. An estimated accuracy depending on the porous Reynolds number or the mean grain diameter is given for the simplified formulation.

References

 
Anderson, D. M., McFadden, G. B., Wheeler, A. A. 1998. Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics, 30: 139–165.
 
Baiocchi, C., Comincioli, V., Magenes, E., Pozzi, G. A. 1973. Free boundary problems in the theory of fluid flow through porous media: existence and uniqueness theorems. Annali Di Matematica Pura Ed Applicata, 97: 1–82.
 
Bardet, J. P., Tobita, T. 2002. A practical method for solving free-surface seepage problems. Computers and Geotechnics, 29: 451–475.
 
Bear, J. 1972. Dynamics of Fluids in Porous Media. New York: American Elsevier Publishing Company.
 
Bruch, J. C. Jr. 1991. Multisplitting and domain decomposition techniques applied to free surface ow through porous media. In: Computational Modelling of Free and Moving Boundary Problems, Vol. 1 Fluid Flow. Wrobel, L. C., Brebbia, C. A. Eds. Computational Mechanics Publications, Walter de Gruyter & Co., Berlin.
 
Chen, Y., Hu, R., Lu, W., Li, D., Zhou, C. 2011. Modeling coupled processes of non-steady seepage flow and non-linear deformation for a concrete-faced rockfill dam. Computers & Structures, 89: 1333–1351.
 
De Lemos, M. J. S., Pedras, M. H. J. 2001. Recent mathematical models for turbulent flow in saturated rigid porous media. Journal of Fluids Engineering, 123: 935–940.
 
De Lemos, M. J. S. 2006. Turbulence in Porous Media. Elsevier Science Ltd.
 
Del Jesus, M., Lara, J. L., Losada, I. J. 2012. Three-dimensional interaction of waves and porous coastal structures: Part I: Numerical model formulation. Coastal Engineering, 64: 57–72.
 
Engelund, F. 1953. On the laminar and turbulent flows of ground water through homogeneous sand. Akademiet for de tekniske videnskaber.
 
Ergun, S. 1952. Fluid flow through packed columns. Chemical Engineering Progress, 48: 89–94.
 
Ferziger, J. H., Peric, M. 2008. Numerische strömungsmechanik. Springer Verlag.
 
Forchheimer, P. 1901. Wasserbewegung durch boden. Z. Ver. Deutsch. Ing., 45: 1782–1788.
 
Gu, Z., Wang, H. 1991. Gravity waves over porous bottoms. Coastal Engineering, 15: 497–524.
 
Harlow, F. H., Welch, J. E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The Physics of Fluids, 8: 2182–2189.
 
Higuera, P., Lara, J. L., Losada, I. J. 2014. Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part I: Formulation and validation. Coastal Engineering, 83: 243–258.
 
Higuera, P. 2015. Application of computational fluid dynamics to wave action on structures. Ph.D. Thesis. Univ. de Cantabria, Santander, Spain.
 
Hirt, C. W., Nichols, B. D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39: 201–225.
 
Hsu, T.-J., Sakakiyama, T., Liu, P. L. F. 2002. A numerical model for wave motions and turbulence flows in front of a composite breakwater. Coastal Engineering, 46: 25–50.
 
Jensen, B., Jacobsen, N. G., Christensen, E. D. 2014. Investigations on the porous media equations and resistance coefficients for coastal structures. Coastal Engineering, 84: 56–72.
 
Kozeny, J. 1927. Über kapillare Leitung des Wassers im Boden. Sitzungberg. Akad. Wiss. Wien, 136: 271–306.
 
Larese, A., Rossi, R., Oñate, E. 2011. Theme B: Simulation of the behavior of prototypes of rockfill dams during overtopping scenarios: Seepage evolution and beginning of failure. In: Proceeding of the 11th Benchmark Workshop on Numerical Analysis of Dams.
 
Larese, A. 2012. A coupled Eulerian–PFEM model for the simulation of overtopping in Rockfill Dams. Ph.D. thesis. International Center for Numerical Methods in Engineering.
 
Larese, A., Rossi, R., Oñate, E. 2015. Finite element modeling of free surface flow in variable porosity media. Archives of Computational Methods in Engineering, 22: 637–653.
 
Lin, P. 1998. Numerical modeling of breaking waves. Ph.D. thesis. Cornell University.
 
Liu, P. L., Lin, P. 1997. A numerical model for breaking waves: The volume of fluid method. Research Report No. CACR-97-02. Cornell University.
 
Liu, P. L. F., Lin, P., Chang, K., Sakakiyama, T. 1999. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125: 322–330.
 
Losada, I. J., Lara, J. L., del Jesus, M. 2016. Modeling the interaction of water waves with porous coastal structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 142: 03116003.
 
Manzke, M. 2019. Development of a scalable method for the efficient simulation of flows using dynamic goal-oriented local grid-adaptation. Ph.D. thesis. Technical University of Hamburg.
 
Mirjalili, S., Jain, S. S., Dodd, M. S. 2017. Interface-capturing methods for two-phase flows: An overview and recent developments. Annual Research Briefs 2017: 117–135.
 
Muzaferija, S., Peric, M. 1998. Computation of free-surface flows using interface-tracking and interface-capturing methods. In: Nonlinear Water Wave Interaction. Mahrenholtz, O., Markiewicz, M. Eds. Computational Mechanics Publications, Southampton.
 
Polubarinova-Kochina, P. Y. 1952. Theory of Ground Water Movement. Princeton University Press.
 
Rhie, C. M., Chow, W. L. 1983. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 21: 1525–1532.
 
Sussman, M., Smereka, P., Osher, S. 1994. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114: 146–159.
 
Tryggvason, G., Scardovelli, R., Zaleski, S. 2011. Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.
 
Ubbink, O. 1997. Numerical prediction of two fluid systems with sharp interfaces. Ph.D. thesis. Department of Mechanical Engineering, Imperial College of Science, London University.
 
Ubbink, O., Issa, R. I. 1999. A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics, 153: 26–50.
 
Uzuoka, R., Borja, R. I. 2012. Dynamics of unsaturated poroelastic solids at finite strain. International Journal for Numerical and Analytical Methods in Geomechanics, 36: 1535–1573.
 
Van Gent, M. R. A. 1992. Formulae to describe porous flow. In: Communications on Hydraulic and Geotechnical Engineering. Report No. 92-2. Delft University of Technology.
 
Van Gent, M. R. A. 1995. Wave interaction with permeable coastal structures. Ph.D. thesis. Faculty of Civil Engineering, Delft University of Technology.
 
Völkner, S., Brunswig, J., Rung, T. 2017. Analysis of non-conservative interpolation techniques in overset grid finite-volume methods. Computers & Fluids, 148: 39–55.
 
Yakubov, S., Maquil, T., Rung, T. 2015. Experience using pressure-based CFD methods for Euler–Euler simulations of cavitating flows. Computers & Fluids, 111: 91–104.
 
Zienkiewicz, O., Xie, Y., Schrefler, B., Ledesma, A., Bicanic, N. 1990. Static and dynamic behaviour of soils: A rational approach to quantitative solutions. II. Semi-saturated problems. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 429: 311–321.
 
Zienkiewicz, O. C., Chan, A., Pastor, M., Schreer, B. A., Shiomi, T. 1999. Computational Soil Dynamics with Special Reference to Earthquake Engineering. Chichester, Wiley.
Experimental and Computational Multiphase Flow
Pages 159-177
Cite this article:
Düsterhöft-Wriggers W, Larese A, Oñate E, et al. Assessment of simplified momentum equations for free surface flows through rigid porous media. Experimental and Computational Multiphase Flow, 2023, 5(2): 159-177. https://doi.org/10.1007/s42757-022-0133-y

759

Views

33

Downloads

1

Crossref

1

Web of Science

1

Scopus

Altmetrics

Received: 30 November 2021
Revised: 22 February 2022
Accepted: 09 March 2022
Published: 22 June 2022
© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Return