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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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A High-Order Conservative Semi-Lagrangian Solver for 3D free surface flows with Sediment Transport on Voronoi Meshes

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Communications on Applied Mathematics and Computation 2023年第2期5卷 596-637页

作者： Matteo Bergami Walter Boscheri Giacomo Dimarco Department of Mathematics and Computer Science University of FerraraVia Machiavelli 30I-44121 FerraraItaly

In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control *** is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous *** presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational *** semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing ***,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be *** accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is *** new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.

关键词： Conservative semi-Lagrangian free surface flows Sediment transport High-order reconstruction Hydrostatic model

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Simulation of free surface flows Based on MapReduce in Cloud Computing

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China Communications 2011年第6期8卷 28-35页

作者：刘旭班晓娟王墨涵 Department of Computer Science and Technology University of Science and Technology

Simulating turbulent liquids with breaking waves and splashes is among the most desired features in fluid animation. Lagrangian methods such as Smoothed Particle Hydrodynamics method (SPH) are a promising way to capture such properties. However, the Particle-based liquid surface simulation has not been applied very well since its consumption is way too large. This paper derives the governing equations in SPH approaches and parallelizes the dynamics-based surface simulation with the MapReduce program models which apply the SPH approach in Cloud Computing. Compared to the serial methods, this approach obtained a 3.11 times speedup on the experimental platform.

关键词： MapReduce SPH cloud computing free surface flows parallelize

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A CONSERVATIVE UNSTRUCTURED STAGGERED GRID SCHEME FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

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Journal of Hydrodynamics 2010年第2期22卷 173-184页

作者： LV Biao JIN Sheng AI Cong-fang State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian 116024China Key Laboratory of Engineering Sediment of Ministry of Communications Tianjin Research Institute for WaterTransport Engineering Tianjin 300456 China

A finite-volume formulation is proposed to solve the three-dimensional,non-hydrostatic Navier-Stokes equations on an unstructured,staggered,z-lever grid,with the goal of simulating non-hydrostatic processes in the free-surface *** advection and diffusion terms in the momentum equation are discretized explicitly with the Eulerian scheme,which has the attractive property of being *** integral method of the top-layer pressure is applied to account for the full effects of non-hydrostatic pressure at the free-surface *** is shown that the results obtained with a small number of vertical layers（e.g.,2-3 layers） are in good agreements with experimental data or analytical solutions,demonstrating the efficiency and accuracy of the model in simulating a range of free-surface flow problems including wave motion and tide-induced motion.

关键词： unstructured staggered grid finite-volume formulation non-hydrostatic free surface flows

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Modelling incompressible flows and fluid-structure interaction problems with smoothed particle hydrodynamics:Briefing on the 2017 SPHERIC Beijing International Workshop

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Journal of Hydrodynamics 2018年第1期30卷 34-37页

作者：刘谋斌黄灿张阿漫 BIC-ESAT College of EngineeringPeking University Ocean Engineering Zhejiang University College of Shipbuilding Engineering Harbin Engineering University

The 2017 SPHERIC Beijing International Workshop（or SPHERIC Beijing 2017） was held at Peking University, in China,on October 17-20, 2017. This is the first time that the SPHERIC Workshop was held out of Europe. We are delighted to present nine contributions in this Special Column of the Journal of Hydrodynamics, and take this opportunity to announce that the 13 th SPHERIC Workshop（or SPHERIC 2018） will be held in Galway, Ireland in 2018 by the National University of Ireland, and the SPHERIC International Workshop in Harbin, China in 2019 by the Harbin Engineering University.

关键词： Smoothed particle hydrodynamic(SPH) SPHERIC free surface flows meshfree methods particle method

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A mathematical model in closed for unsteady mixed flows water pipes Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Science China Mathematics 2012年第2期55卷 221-244页

作者： BOURDARIAS Christian ERSOY Mehmet GERBI Stephane Laboratoire de Mathdmatiques Universitd de Savoie Le Bourget du Lac 73376 France Basque Center for Applied Mathematics Bizkaia Technology Park Derio Basque Country 48160 Spain Institut des Mathematiques de Toulon et du Vat Universite du Sud Toulon-Var La Garde Cedex 83957 France

We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes. In the case of free surface incompressible flows, the FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the P-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope with the transition between a free surface state and a pressured （i.e., compressible） state, we propose a mixed model, the PFS-model, taking into account changes of section and slope variation.

关键词： shallow water equations unsteady mixed flows free surface flows pressurized flows curvilinear transformation asymptotic analysis

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Simulation of Three-Dimensional Benard-Marangoni flows Including Deformed surfaces

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Communications in Computational Physics 2009年第2期5卷 273-295页

作者： Tormod Bjøntegaard Einar M.Rønquist Department of Mathematical Sciences Norwegian University of Science and TechnologyN-7491 TrondheimNorway

We present a coupled thermal-fluid model for Benard-Marangoni convection in a three-dimensional fluid *** governing equations are derived in detail for two reasons:first,we do not assume a flat free surface as commonly done;and second,we prepare for the use of flexible *** governing equations are discretized using spectral elements in space and an operator splitting approach in *** we are here primarily interested in steady state solutions,the focus is on the spatial *** overall computational approach is very attractive to use for several reasons:(i)the solution can be expected to have a high degree of regularity,and rapid convergence can be expected;(ii)the spectral element decomposition automatically gives a convenient parameterization of the free surface that allows powerful results from differential geometry to easily be exploited;(iii)free surface deformation can readily be included;(iv)both normal and tangential stresses are conveniently accounted for through a single surface integral;(v)no differentiation of the surface tension is necessary in order to include thermocapillary effects(due to integration-byparts twice);(vi)the geometry representation of the free surface need only be C0 across element boundaries even though curvature effects are ***-dimensional simulation results are presented,including the free surface deflection due to buoyancy and thermocapillary effects.

关键词： Benard-Marangoni free surface flows differential geometry spectral elements

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