Volume 29, Issue 6
A Numerthod for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D

Kirill D. Nikitin, Maxim A. Olshanskii, Kirill M. Terekhov & Yuri V. Vassilevski

J. Comp. Math., 29 (2011), pp. 605-622

Published online: 2011-12

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  • 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.

  • Keywords

Free surface flows Viscoplastic fluid Adaptive mesh refinement Octree meshes

  • AMS Subject Headings

65M06 76D27 76D99.

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COPYRIGHT: © Global Science Press

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@Article{JCM-29-605, author = {}, title = {A Numerthod for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {6}, pages = {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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1109-m11si01}, url = {http://global-sci.org/intro/article_detail/jcm/8496.html} }
TY - JOUR T1 - A Numerthod for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D JO - Journal of Computational Mathematics VL - 6 SP - 605 EP - 622 PY - 2011 DA - 2011/12 SN - 29 DO - http://doi.org/10.4208/jcm.1109-m11si01 UR - https://global-sci.org/intro/article_detail/jcm/8496.html KW - Free surface flows KW - Viscoplastic fluid KW - Adaptive mesh refinement KW - Octree meshes AB - 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.
Kirill D. Nikitin, Maxim A. Olshanskii, Kirill M. Terekhov & Yuri V. Vassilevski. (1970). A Numerthod for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D. Journal of Computational Mathematics. 29 (6). 605-622. doi:10.4208/jcm.1109-m11si01
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