A spectral method is developed to study the steady and unsteady flow of fluid into a line sink from a horizontally confined aquifer, and the results are compared to solutions obtained implementing the finite element package COMSOLTM. The aquifer or drain is considered to be confined below so that the solutions are fundamentally unsteady. Comparison is made between the two methods in determining the drawdown of the surface.

The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.

Experiments are presented on the deformation of free surface induced by water exit of axisymmetric bodies, particular at the moment before body detaching from water. A set of experimental apparatus is designed to provide driving force for the bodies. A high-speed camera is adopted to capture the motion and deformation of the free surface. Bodies of various shapes, including a stretched spheroid, a sphere, a circular cone and a combination of cylinder and circular cone, are lifted out of water with different velocities, by using a straight rod attached on the top of models. It is found that free-surface deformation is affected by the moving velocity a lot. Three wake flow or free-surface spike patterns are generated corresponding to different velocities. When the velocity is larger than a critical velocity, cavitation incepts and bubble is entrapped inside the water spike, which changes the flow pattern and shape of the spike. It is aimed to explore the spike phenomenon of free surface and explain the reasons behind it.

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

Problems of wave interaction with a body with arbitrary shape floating or submerged in water are of immense importance in the literature on the linearized theory of water waves. Wave-free potentials are used to construct solutions to these problems involving bodies with circular geometry, such as a submerged or half-immersed long horizontal circular cylinder (in two dimensions) or sphere (in three dimensions). These are singular solutions of Laplace’s equation satisfying the free surface condition and decaying rapidly away from the point of singularity. Wave-free potentials in two and three dimensions for infinitely deep water as well as water of uniform finite depth with a free surface are known in the literature. The method of constructing wave-free potentials in three dimensions is presented here in a systematic manner, neglecting or taking into account the effect of surface tension at the free surface or for water with an ice cover modelled as a thin elastic plate floating on the water. The forms of the wave motion at the upper surface (free surface or ice-covered surface) related to these wave-free potentials are depicted graphically in a number of figures for all the cases considered.

We present a study of the forces during free-surface water entry of spheres of varying masses, diameters, and surface treatments. Previous studies have shown that the formation of a subsurface air cavity by a falling sphere is conditional upon impact speed and surface treatment. This study focuses on the forces experienced by the sphere in both cavity-forming and non-cavity-forming cases. Unsteady force estimates require accurate determination of the deceleration for both high and low mass ratios, especially as inertial and hydrodynamic effects approach equality. Using high-speed imaging, high-speed particle image velocimetry, and numerical simulation, we examine the nature of the forces in each case. The effect of mass ratio is shown, where a lighter sphere undergoes larger decelerations and more dramatic trajectory changes. In the non-cavity-forming cases, the forces are modulated by the growth and shedding of a strong, ring-like vortex structure. In the cavity-forming cases, little vorticity is shed by the sphere, and the forces are modulated by the unsteady pressure required for the opening and closing of the air cavity. A data-driven boundary-element-type method is developed to accurately describe the unsteady forces using cavity shape data from experiments.

We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems.

We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [J.L. Bona, T. Colin and D. Lannes,Arch. Ration. Mech. Anal. 178 (2005) 373–410] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussinesq system displayed in [W. Choi and R. Camassa, J. Fluid Mech. 313 (1996) 83–103]. We study the well-posedness of such systems, and the asymptotic convergence of their solutions towards solutions of the full Euler system. Then, we provide a rigorous justification of the so-called KdV approximation, stating that any bounded solution of the full Euler system can be decomposed into four propagating waves, each of them being well approximated by the solutions of uncoupled Korteweg-de Vries equations. Our method also applies for models with the rigid lid assumption, using the Boussinesq/Boussinesq models introduced in [J.L. Bona, D. Lannes and J.-C. Saut, J. Math. Pures Appl. 89 (2008) 538–566]. Our explicit and simultaneous decomposition allows to study in details the behavior of the flow depending on the depth and density ratios, for both the rigid lid and free surface configurations. In particular, we consider the influence of the rigid lid assumption on the evolution of the interface, and specify its domain of validity. Finally, solutions of the Boussinesq/Boussinesq systems and the KdV approximation are numerically computed, using a Crank-Nicholson scheme with a predictive step inspired from [C. Besse,C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 1427–1432;C. Besse and C.H. Bruneau,Math. Mod. Methods Appl. Sci. 8 (1998) 1363–1386].

An efficient finite difference framework based on moving meshes methods is developed for the three-dimensional free surface viscoelastic flows. The basic model equations are based on the incompressible Navier-Stokes equations and the Oldroyd-B constitutive model for viscoelastic flows is adopted. A logical domain semi-Lagrangian scheme is designed for moving-mesh solution interpolation and convection. Numerical results show that harmonic map based moving mesh methods can achieve better accuracy for viscoelastic flows with free boundaries while using much less memory and computational time compared to the uniform mesh simulations.

The standard multilayer Saint-Venant system consists in introducing fluidlayers that are advected by the interfacial velocities. As a consequence there is no massexchanges between these layers and each layer is described by its height and its averagevelocity.Here we introduce another multilayer system with mass exchanges between the neighboringlayers where the unknowns are a total height of water and an average velocity per layer.We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy andhyperbolicity properties of the model. We also give a kinetic interpretation leading toeffective numerical schemes with positivity and energy properties. Numerical tests showthe versatility of the approach and its ability to compute recirculation cases with windforcing.

Dans ce travail, une étude bidimensionnelle du moulage par gravité avec coulée en source est entreprise par voie de simulation numérique. Le but de l'étude est de montrer les principales causes de la formation des soufflures dans les pièces moulées avec un tel procédé. La première partie de notre travail est consacrée à l'étude du jet libre à partir d'un bassin en vue d'optimiser la forme de la descente de coulée. Dans la deuxième partie, nous avons entrepris la simulation du remplissage d'un moule rectangulaire. Les équations de continuité, de mouvement et de matière régissant le comportement hydrodynamique du métal coulé, ont été résolues par la méthode des volumes finis. Pour prédire l'évolution du front de matière, la méthode de Volume de Fluide VOF a été utilisée. Nous avons analysé l'influence de la hauteur du bassin sur la forme du jet, et nous avons montré dans le cas de la coulée en source, l'importance de l'inclinaison de la surface des descentes du système d'attaque. Aussi, dans ce travail, nous avons étudié l'évolution temporelle de l'écoulement liquide au cours du remplissage d'une cavité rectangulaire en fonction de la vitesse de remplissage. Nous avons trouvé que l'augmentation du débit de coulage favorise la formation des pièges d'air ce qui engendre inévitablement des soufflures dans la pièce finale. Les résultats numériques obtenus sont validés par des comparaisons avec des résultats analytiques et expérimentaux antérieurs.

Cet article présente la simulation d'écoulements autour decorps en mouvement basée sur un solveur Navier-Stokes utilisant destechniques d'adaptation locale de maillage.Après une description des méthodes utilisées, une application à l'étude d'impacts sera présentée. On mettra en évidencel'intérêt de l'adaptation locale de maillage dans ce type de simulation,notamment pour la capture précise des pics de pression engendrés lors des impacts.