Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Adaptive finite element simulation of three-dimensional surface tension dominated free-surface flow problems

An arbitrary Lagrangian--Eulerian finite element method is described for the solution of time-dependent, three-dimensional, free-surface flow problems. Many flows of practical significance involve contact lines, where the free surface meets a solid boundary. This contact line may be pinned to a particular part of the solid but is more typically free to slide in a manner that is characterised by the dynamic contact angle formed by the fluid. We focus on the latter case and use a model that admits spatial variation of the contact angle: thus permitting variable wetting properties to be simulated. The problems are driven by the motion of the fluid free surface (under the action of surface tension and external forces such as gravity) hence the geometry evolves as part of the solution, and mesh adaptivity is required to maintain the quality of the computational mesh for the physical domain. Continuous mesh adaptivity, in the form of a pseudo-elastic mesh movement scheme, is used to move the interior mesh nodes in response to the motion of the fluid's free surface. Periodic, discrete remeshing stages are also used for cases in which the fluid volume has grown, or is sufficiently distorted, by the free-surface motion. Examples are given of a droplet sliding on an inclined uniform plane and of a droplet spreading on a surface with variable wetting properties

Mesh-free simulation of complex LCD geometries

We use a novel mesh-free simulation approach to study the post aligned bistable nematic (PABN) cell. By employing the Qian-Sheng formalism for liquid crystals along with a smooth representation of the surface posts, we have been able to identify two distinct stable configurations. The three-dimensional order field configurations of these states and their elastic free energies are consistent with both experimental results and previous simulation attempts. However, alternative states suggested in previous studies do not appear to remain stable when finite post curvature is considered.</p

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillarywave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfv{\'e}n wave turbulence. Although surface waves on a magnetic fluid are different from Alfv{\'e}n waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.Comment: in press in Phys. Rev E (Letter). For Supplemental Material, see http://www.msc.univ-paris-diderot.fr/~falcon/PRE\_Letter22/PRE2022andSuppMat.pd

Simulation of Free Surface Compressible Flows Via a Two Fluid Model

The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In such a numerical model, the free surface becomes a thin three dimensional zone. The present method has at least three advantages: (i) the free-surface treatment is completely implicit; (ii) it can naturally handle wave breaking and other topological changes in the flow; (iii) one can easily vary the Equation of States (EOS) of each fluid (in principle, one can even consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for reasonable EOS.Comment: 8 pages, 10 figures; OMAE2008, 27th International Conference on Offshore Mechanics and Arctic Engineering. Other authors papers and animations related to this work can be downloaded from: http://www.cmla.ens-cachan.fr/fileadmin/Membres/dutykh/ The paper was slightly modified according to referees comment

Selective solvation in aqueous mixtures: Interface deformations and instability

We briefly review the effects of selective solvation of ions in aqueous mixtures, where the ion densities and the composition fluctuations are strongly coupled. We then examine the surface tension \gamma of a liquid-liquid interface in the presence of ions. We show that \gamma can be decreased drastically due to the electrostatic and solvation interactions near the interface. We calculate how the free energy is changed due to small surface undulations in the presence of an electric double layer. A surface instability occurs for negative \gamma, which can easily be realized for antagonistic ion pairs near the solvent criticality. Three-dimensional simulation shows how the surface instability is induced.Comment: 16 pages, 4 figure

Simple free-surface detection in two and three-dimensional SPH solver

A simple free-surface particle detection method for two and three-dimensional SPH simulation has been implemented. The method uses sphere representation for the SPH particle. The fluid domain is covered by overlapping spheres. A sphere whose surface is not fully covered considered as boundary. To test particle boundary status, we used a sum of normalized relative position vectors from neighbouring particles to the test particle. By checking the existence of un- covered sphere surface by this vector sum, boundary status of the test particle can be determined. This boundary detection method can be easily embedded in the SPH solver algorithm.Comment: 10 pages, 11 figures, Selected Paper from the International Symposium on Computational Science 201

Three-Dimensional Smoothed Particle Hydrodynamics Method for Simulating Free Surface Flows

In this paper, we applied an improved Smoothing Particle Hydrodynamics (SPH) method by using gradient kernel renormalization in three-dimensional cases. The purpose of gradient kernel renormalization is to improve the accuracy of numerical simulation by improving gradient kernel approximation. This method is implemented for simulating free surface flows, in particular dam break case with rigid ball structures and the propagation of waves towards a slope in a rectangular tank.Comment: 9 pages, 5 figures, Selected Paper from the International Symposium on Computational Science 201