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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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