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A numerical method for the simulation of free surface flows with surface tension
 Computers and Fluids
"... A numerical model for the simulation of threedimensional liquidgas flows with free surfaces and surface tension is presented. The incompressible NavierStokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas ..."
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A numerical model for the simulation of threedimensional liquidgas flows with free surfaces and surface tension is presented. The incompressible NavierStokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface. An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquidgas interface, the method described in [5] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh. The model is validated and numerical results in two and three space dimensions
Computing and Visualization in Science manuscript No. (will be inserted by the editor) On the Modeling and Simulation of NonHydrostatic Dam Break Flows
"... Abstract. The numerical simulation of threedimensional dam break flows is discussed. A nonhydrostatic numerical model for freesurface flows is considered, which is based on the incompressible NavierStokes equations coupled with a volumeoffluid approach. The numerical results obtained for a ..."
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Abstract. The numerical simulation of threedimensional dam break flows is discussed. A nonhydrostatic numerical model for freesurface flows is considered, which is based on the incompressible NavierStokes equations coupled with a volumeoffluid approach. The numerical results obtained for a variety of benchmark problems show the validity of the numerical approach, in comparison with other numerical models, and allow to investigate numerically the nonhydrostatic threedimensional effects, in particular for the usual test cases where hydrostatic approximations are known analytically. The numerical experiments on actual topographies, in particular the Malpasset dam break and the (hypothetical) break of the GrandeDixence dam in Switzerland, also illustrate the capabilities of the method for largescale simulations and reallife visualization. Key words Freesurface hydrodynamical flows, Hy
Arbitrary Lagrangian–Eulerian method for
, 2004
"... Numerical simulation of twodimensional viscous incompressible fluid with free boundaries is getting more attention for the past few decades; these types of problems arise frequently in several important industrial applications, such as melting and solidification, crystal growth, glass and metal for ..."
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Numerical simulation of twodimensional viscous incompressible fluid with free boundaries is getting more attention for the past few decades; these types of problems arise frequently in several important industrial applications, such as melting and solidification, crystal growth, glass and metal forming processes, etc. In particular, modeling of mould filling during the casting of metals into moulds is an example
Numerical analysis and simulation of the dynamics of mountain glaciers
"... Abstract In this paper, we analyse and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solution are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stoke ..."
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Abstract In this paper, we analyse and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solution are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice which describes the time evolution of a glacier. The accumulation due to snow precipitation and the melting are accounted in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a twogrids method. As an illustration, we simulate Aletschgletscher, Switzerland, over the 21st century by using realistic climatic conditions.
On the Modeling and Simulation of NonHydrostatic Dam Break Flows
, 2013
"... The numerical simulation of threedimensional dam break flows is discussed. A nonhydrostatic numerical model for freesurface flows is considered, which is based on the incompressible NavierStokes equations coupled with a volumeoffluid approach. The numerical results obtained for a variety of be ..."
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The numerical simulation of threedimensional dam break flows is discussed. A nonhydrostatic numerical model for freesurface flows is considered, which is based on the incompressible NavierStokes equations coupled with a volumeoffluid approach. The numerical results obtained for a variety of benchmark problems show the validity of the numerical approach, in comparison with other numerical models, and allow to investigate numerically the nonhydrostatic threedimensional effects, in particular for the usual test cases where hydrostatic approximations are known analytically. The numerical experiments on actual topographies, in particular the Malpasset dam break and the (hypothetical) break of the GrandeDixence dam in Switzerland, also illustrate the capabilities of the method for largescale simulations and reallife visualization.
Archives of Computational Methods in Engineering State of the art reviews Numerical Simulation of TwoPhase Free Surface Flows
"... Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volumeoffluid method is used for the numerical simulation of twophase fre ..."
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Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volumeoffluid method is used for the numerical simulation of twophase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible NavierStokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a twogrids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized. 1
Marco Picasso
"... Abstract A model for the simulation of complex threedimensional free surface flows is presented. An incompressible liquid interacts with a compressible gas. The incompressible NavierStokes equations are solved only in the liquid domain while the dynamical effects in the gas are neglected. The comp ..."
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Abstract A model for the simulation of complex threedimensional free surface flows is presented. An incompressible liquid interacts with a compressible gas. The incompressible NavierStokes equations are solved only in the liquid domain while the dynamical effects in the gas are neglected. The compressibility effects of the gas are taken into account by computing its pressure. Surface tension effects are added on the interface. A volumeoffluid method is used to track the liquid domain. A time splitting scheme together with a twogrids method allows to decouple the computation of the gas pressure and surface tension effects from the resolution of advection and diffusion equations in the liquid domain. Numerical results are presented in order to validate the model. Keywords: Volumeoffluid, Free surface flows, Twogrids, Incompressible liquid, Compressible gas
A Numerical Method for Fluid Flows with Complex Free Surfaces
"... Summary. A numerical method for the simulation of fluid flows with complex free surfaces is presented. The liquid is assumed to be a Newtonian or a viscoelastic fluid. The compressible effects of the surrounding gas are taken into account, as well as surface tension forces. An Eulerian approach base ..."
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Summary. A numerical method for the simulation of fluid flows with complex free surfaces is presented. The liquid is assumed to be a Newtonian or a viscoelastic fluid. The compressible effects of the surrounding gas are taken into account, as well as surface tension forces. An Eulerian approach based on the volumeoffluid formulation is chosen. A time splitting algorithm, together with a twogrids method, allows the various physical phenomena to be decoupled. A chronological approach is adopted to highlight the successive improvements of the model and the wide range of applications. Numerical results show the potentialities of the method. 1
Numerical Simulation of Bubbles under an Inclined Plane: Application to Aluminum Electrolysis 1
"... The numerical investigation of large bubbles rising under an inclined plane is presented. A numerical method for the simulation of fluid flows with complex free surfaces is presented, in which the liquid is assumed to be Newtonian, while gas bubbles are assumed to be compressible. A volumeoffluid ..."
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The numerical investigation of large bubbles rising under an inclined plane is presented. A numerical method for the simulation of fluid flows with complex free surfaces is presented, in which the liquid is assumed to be Newtonian, while gas bubbles are assumed to be compressible. A volumeoffluid method is used to track the liquid domain. A time splitting algorithm allows to decouple the advection and diffusion operators, the compressibility effects in the gas, and the surface tension effects. Finite element techniques are coupled with a characteristics method with a two grids method. Numerical simulations are in excellent agreement with experimental data. Key words