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A NUMERICAL METHOD FOR THE SIMULATION OF FREE SURFACE FLOWS OF viscoplastic fluid IN 3D

Journal of Computational Mathematics 2011年第6期29卷 605-622页

作者： Kirill D. Nikitin Maxim A. Olshanskii Kirill M. Terekhov Yuri V. Vassilevski Institute of Numerical Mathematics Russian Academy of Sciences Moscow Russia Department of Mechanics and Mathematics Moscow State University Moscow Russia

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 regu- larized 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.

关键词： Free surface flows viscoplastic fluid Adaptive mesh refinement Oetree meshes.

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Flow of a viscoplastic fluid on a Rotating Disk

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Applied Mathematics and Mechanics(English Edition) 1994年第5期15卷 447-453页

作者：范椿 Institute of Mechanics Academia Sinica Beijing

The equations describing the flow of a viscoplastic fluid on a rotating disk are de-rived and are solved by perturbation technique and nurmerical computation respectivelyfor 2 cases. This makes it possible to calculate the thickness distribution of film. Twokinds of distribution of thickness have been found. For the viscoplastic fluid for whichboth viscosity and yield stress are independent of radial coordinate r, the thickness hdecreases with increasing r. For a Bingham fluid for which both viscosity and yieldstress are function of time and r. the thickness h increases with increasing r.

关键词： flow on a rotating disk viscoplastic fluid thickness distributionof film

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Observations on sand jets in viscoplastic fluids

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Theoretical & Applied Mechanics Letters 2012年第5期2卷 23-28页

作者： David Z.Zhu N.Rajaratnam Deptartment of Civil and Environmental Engineering University of Alberta

Sand jet in non-Newtonian viscoplastic fluid is associated with a number of industrial and engineering applications, including sand capping for the reclamation of oilsands railings ponds and sediment deposition into soft mud. In this study, several experiments were carried out by depositing circular sand jets vertically into viscoplastic fluids, known as Laponite gel. The deformation regimes of sand jets in the gel were investigated. The yield-gravity parameter of the deformed sand drop in the gel was computed.

关键词： non-Newtonian fluid viscoplastic fluid granular flow sand jet

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