Close Search Advanced
Journals
Resources
About Us
Open Access

A Numerical Method for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D

A Numerical Method for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D
Preview
Add to basket

Year:    2011

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 6 : pp. 605–622

Abstract

In this paper we study a numerical method for the simulation of free surface flows of viscoplastic (Herschel-Bulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. A regularized model is applied to handle the non-differentiability of the constitutive relations. We consider an extension of the stable approximation of the Newtonian flow equations on staggered grid to approximate the viscoplastic model and level-set equations if the free boundary evolves and the mesh is dynamically refined or coarsened. The numerical method is first validated for a Newtonian case. In this case, the convergence of numerical solutions is observed towards experimental data when the mesh is refined. Further we compute several 3D viscoplastic Herschel-Bulkley fluid flows over incline planes for the dam-break problem. The qualitative comparison of numerical solutions is done versus experimental investigations. Another numerical example is given by computing the freely oscillating viscoplastic droplet, where the motion of fluid is driven by the surface tension forces. Altogether the considered techniques and algorithms (the level-set method, compact discretizations on dynamically adapted octree cartesian grids, regularization, and the surface tension forces approximation) result in efficient approach to modeling viscoplastic free-surface flows in possibly complex 3D geometries.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1109-m11si01

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 6 : pp. 605–622

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Free surface flows Viscoplastic fluid Adaptive mesh refinement Octree meshes.

  1. Modeling of flow performance of self-consolidating concrete using Dam Break Theory and computational fluid dynamics

    Hosseinpoor, Masoud | Yahia, Ammar | Khayat, Kamal H.

    Cement and Concrete Composites, Vol. 102 (2019), Iss. P.14

    https://doi.org/10.1016/j.cemconcomp.2019.04.018 [Citations: 8]
  2. Numerical Mathematics and Advanced Applications - ENUMATH 2013

    A Unified Approach for Computing Tsunami, Waves, Floods, and Landslides

    Danilov, Alexander | Nikitin, Kirill | Olshanskii, Maxim | Terekhov, Kirill | Vassilevski, Yuri

    2015

    https://doi.org/10.1007/978-3-319-10705-9_63 [Citations: 0]

  3. An octree-based adaptive semi-Lagrangian VOF approach for simulating the displacement of free surfaces

    Laurmaa, Viljami | Picasso, Marco | Steiner, Gilles

    Computers & Fluids, Vol. 131 (2016), Iss. P.190

    https://doi.org/10.1016/j.compfluid.2016.03.005 [Citations: 13]

  4. A simplified depth-averaged debris flow model with Herschel-Bulkley rheology for tracking density evolution: a finite volume formulation

    Kang, Dong Hun | Hong, Moonhyun | Jeong, Sangseom

    Bulletin of Engineering Geology and the Environment, Vol. 80 (2021), Iss. 7 P.5331

    https://doi.org/10.1007/s10064-021-02202-9 [Citations: 9]

  5. Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

    Fernández-Nieto, Enrique D. | Gallardo, José M. | Vigneaux, Paul

    Journal of Computational Physics, Vol. 264 (2014), Iss. P.55

    https://doi.org/10.1016/j.jcp.2014.01.026 [Citations: 12]

  6. Progress on numerical simulation of yield stress fluid flows (Part I): Correlating thermosolutal coefficients of Bingham plastics within a porous annulus of a circular shape

    Ragui, Karim | Boutra, Abdelkader | Bennacer, Rachid | Khaled Benkahla, Youb

    International Journal of Heat and Mass Transfer, Vol. 126 (2018), Iss. P.72

    https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.010 [Citations: 15]

  7. Scalable Local Timestepping on Octree Grids

    Fernando, Milinda | Sundar, Hari

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 2 P.C156

    https://doi.org/10.1137/20M136013X [Citations: 0]

  8. Finite stopping times for freely oscillating drop of a yield stress fluid

    Cheng, Wanli | Olshanskii, Maxim A.

    Journal of Non-Newtonian Fluid Mechanics, Vol. 239 (2017), Iss. P.73

    https://doi.org/10.1016/j.jnnfm.2016.12.001 [Citations: 3]

  9. Progress in numerical simulation of yield stress fluid flows

    Saramito, Pierre | Wachs, Anthony

    Rheologica Acta, Vol. 56 (2017), Iss. 3 P.211

    https://doi.org/10.1007/s00397-016-0985-9 [Citations: 122]

  10. An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

    Nikitin, Kirill | Vassilevski, Yuri | Yanbarisov, Ruslan

    Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 36 (2021), Iss. 3 P.165

    https://doi.org/10.1515/rnam-2021-0014 [Citations: 1]

  11. Modeling of spillage and debris floods as Newtonian and viscoplastic Bingham flows with free surface with mixed stabilized finite elements

    Moreno, Elvira | Dialami, Narges | Cervera, Miguel

    Journal of Non-Newtonian Fluid Mechanics, Vol. 290 (2021), Iss. P.104512

    https://doi.org/10.1016/j.jnnfm.2021.104512 [Citations: 5]

  12. Viscoplastic dam-breaks

    Valette, R. | Pereira, A. | Riber, S. | Sardo, L. | Larcher, A. | Hachem, E.

    Journal of Non-Newtonian Fluid Mechanics, Vol. 287 (2021), Iss. P.104447

    https://doi.org/10.1016/j.jnnfm.2020.104447 [Citations: 10]

  13. Information model of the impact of avalanche snow masses on the elements of the landscape infrastructure

    Soloviev, A S | Kalach, A V | Desyatov, D B | Rossihina, L V

    Journal of Physics: Conference Series, Vol. 1202 (2019), Iss. P.012015

    https://doi.org/10.1088/1742-6596/1202/1/012015 [Citations: 1]

  14. An adaptive octree finite element method for PDEs posed on surfaces

    Chernyshenko, Alexey Y. | Olshanskii, Maxim A.

    Computer Methods in Applied Mechanics and Engineering, Vol. 291 (2015), Iss. P.146

    https://doi.org/10.1016/j.cma.2015.03.025 [Citations: 37]

  15. An adaptive variational finite difference framework for efficient symmetric octree viscosity

    Goldade, Ryan | Wang, Yipeng | Aanjaneya, Mridul | Batty, Christopher

    ACM Transactions on Graphics, Vol. 38 (2019), Iss. 4 P.1

    https://doi.org/10.1145/3306346.3322939 [Citations: 18]

  16. Run-Up Simulation of Impulse-Generated Solitary Waves

    Laurmaa, Viljami | Picasso, Marco | Steiner, Gilles | Evers, Frederic M. | Hager, Willi H.

    Journal of Engineering Mechanics, Vol. 144 (2018), Iss. 2

    https://doi.org/10.1061/(ASCE)EM.1943-7889.0001385 [Citations: 2]

  17. Computer modeling and measurement of devastating impact characteristics of snow avalanches

    Solovyev, A. S. | Kalach, A. V. | Desyatov, D. B.

    2017 2nd International Ural Conference on Measurements (UralCon), (2017), P.168

    https://doi.org/10.1109/URALCON.2017.8120705 [Citations: 0]

  18. An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

    Olshanskii, Maxim A. | Terekhov, Kirill M. | Vassilevski, Yuri V.

    Computers & Fluids, Vol. 84 (2013), Iss. P.231

    https://doi.org/10.1016/j.compfluid.2013.04.027 [Citations: 32]