Numerical Analysis of Nonlinear Water Waves Using Arbitrary Lagrangian-Eulerian Finite Element Method.

Arbitrary Lagrangian–Eulerian finite element analysis of free surface flow using a velocity–vorticity formulation

Chapter 6 - Free Surface and Buoyancy Driven Flows

A diffuse interface method for complex three-dimensional free surface flows

A five-equation model based global ale method for compressible multifluid and multiphase flows

The Arbitrary Lagrangian-Eulerian (ALE) method is used in a variety of engineering and scientific applications for enabling multi-physics simulations. Unfortunately, the ALE method can suffer from simulation failures that require users to adjust parameters iteratively in order to complete a simulation. In this paper, we present a supervised learning framework for predicting conditions leading to simulation failures. To our knowledge, this is the first time machine learning has been applied to ALE simulations. We propose a novel learning representation for mapping the ALE domain onto a supervised learning formulation. We analyze the predictability of these failures and evaluate our framework using well-known test problems.

An MLSPH algorithm for free surface flows in engineering applications

In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian–Eulerian (ALE) approach. For that purpose we introduce the ALE‐sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd.

The parachute inflation process is a typical time-varying, non-linear and fluid-structure coupling problem, especially inairdrop condition. For its complexity, numerical model of the inflation process is a big challenge, and most of the modelsestablished before still have room for improvement. There were two common problems that the first one was ignoranceof inertia force of canopy and line, and the second was that took stretch speed as the initial airdrop speed in modelling.Thus, a modified finite element model for canopy inflation process based on ALE (Arbitrary Lagrange Euler) method wasestablished that the inertia force of canopy and line was taken into consideration and the initial airdrop speed wasestimated and adjusted. The opening load in finite mass situation during deployment-inflation process of C-9 typeparachute was calculated. The result was compared to experimental data and calculated data of unmodified models. Itwas indicated that the opening load and peak time of modified model was the closest to experiment and the snatch loadwas also calculated and confirmed, so that the correctness and rationality of the model was verified. Then the factorinfluence of inertia force and initial airdrop speed was analysed, which provided a reference for parachute numericalmodelling.

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

The dynamic numerical modeling theory and wave impact calculation method of gasbag type floating bridge (GTFB) were studied by using the multi-material Arbitrary Lagrangian-Eulerian (ALE) method and penalty function method. The air and seawater were described by the ALE method, the structure of floating bridge was described by the Lagrangian method and the coupling force between floating bridge and flow field was calculated by penalty function method. The floating bridge-fluid coupling models were established by HyperMesh software. Then, the models and calculation parameters were validated. The structural responses of the GTFB under solitary wave impacting were analyzed. The results show that the maximum contact force of hinge and maximum stress of gasbag appeared at the ends of the floating bridge, and the maximum bending moment of hinge appeared in the middle section.

Numerical solution of the Giesekus model for incompressible free surface flows without solvent viscosity

Up to now, no a real liquid metal (LM) free surface flow have been successfully used in magnetic fusion devices as MHD instability and unavoidable rivulet flow. Recently, after we carried out a guidable free curve-surface flow on theoretically and experimentally, seeking for other way to get a full-cover free surface flow is also in implementing. The superficial layer MHD effect in free surface flow is experimentally observed. After compared and analyzed the characteristic parameters of the free surface flow, the new two parameters of surface cover ratio and rivulet flow index are introduced to characterize the flowing characteristic of the full-cover free surface flow under magnetic field. According to the analysis rule, for different liquid metal, there are the different unique conditions to meet full-cover free surface flow under magnetic field.

Nonlinear solutions of free surface flow under a sluice gate are studied. Upstream, the fluid is assumed to be infinitely deep, and the gate is at an angle to the horizontal axis. The flow emerges from the gate and produces a uniform flow far downstream. The problem is solved numerically by a boundary element method derived from an integral equation along the free surface. An analytical function is constructed, related to the upstream flow, so that the integral equation is solvable. As a result, a free surface flow with smooth detachment from the edge of the gate is obtained for relatively large upstream Froude numbers. As the Froude number decreases, a free surface with back flow near the edge of the gate occurs, until at a certain Froude number a stagnation point occurs. References D. D. Frangmeier, T. S. Strelkoff, Solution for gravity flow under a sluice gate, ASCE J. Engng. Mech. Div. , 94 , 1968, 153--176. B. E. Lorock, Gravity-affected flow from planer sluice gate, ASCE J. Engng. Mech. Div. , 96 , 1969, 1211--1226. Y. K. Chung, Solution of flow under sluice gates, ASCE J. Engng. Mech. Div. , 98 , 1972, 121--140. J. Asavanant, J.-M. Vanden-Broeck, Nonlinear free surface flows emerging from vessels and flows under a sluice gate, J. Austral. Math. Soc. , 38 , 1996, 63--86. doi:10.1017/S0334270000000473 J.-M. Vanden-Broeck, Numerical calculations of the free-surface flow under a sluice gate, J. Fluid Mech. , 330 , 1996, 339--347. http://journals.cambridge.org/abstract_S0022112096003849 B. J. Binder, J.-M. Vanden-Broeck, Free surface flows past surfboards and sluice gates, Eur. J. Appl. Maths. , 16 , 2005, 601--619 doi:10.1017/S0956792505006443 B. J. Binder, J.-M. Vanden-Broeck, The effect of disturbances on the flows under a sluice gate and past an inclined plate, J. Fluid Mech. , 576 , 2007, 475--490 doi:10.1017/S0022112007004806 J.-M. Vanden-Broeck, E. O. Tuck, Flow near the interaction of a free surface with a vertical wall, SIAM J. Appl. Math. , 54 , 1994, 1--33. doi:10.1137/S0036139992240838 L. H. Wiryanto, J. Widjaja, B. Supriyanto, Free-surface flow under a sluice gate from deep water, Bul. Malay. Math. Soc. , 34 , 2011, 601--609. http://www.emis.de/journals/BMMSS/vol34_3_17.html L. H. Wiryanto, E. O. Tuck, A back-turning jet formed by a uniform shallow stream hitting a vertical wall, Proc. Int. Conf. on Dif. Eqs. , Kluwer Academic Press, 1997. L. H. Wiryanto, E. O. Tuck, An open-channel flow meeting a barrier and forming one or two jets, J. Austral. Math. Soc. , 41 , 2000, 458--472. doi:10.1017/S0334270000011760 L. H. Wiryanto, Small Froude number solutions of flow caused by a line source, J. Indones. Math. Soc. , 6 , 2000, 1--6. G. C. Hocking, L. K. Forbes, A note on the flow induced by a line sink beneath a free surface, J. Austral. Math. Soc. B , 32 , 1991, 251--260. doi:10.1017/S0956792507006924 G. C. Hocking, L. K. Forbes, Subcritical free-surface flow caused by a line source in a fluid of finite depth, J. Eng. Math. , 26 , 1992, 455--466. doi:10.1007/BF00042763 L. H. Wiryanto, Zero gravity of a jet emerging from a slit, J. Indones. Math. Soc. , 12 , 2006, 89--98. L. M. Milne-Thomson, Theoretical hydrodynamics . Dover Publications, Inc., 1968, 274--281.

In this paper, we performed needle insertion simulation considering needle tip shape by Arbitrary Lagrangian-Eulerian (ALE) method. ALE method is suitable for the large deformation and a fracture. To evaluate developed model, we compared the needle deflection between experimental results and simulation results. As a result, errors in each needle between both results were less than 3 mm.

We describe here our newly developed ALE code on 2D quadrilaterals. The code is employed here in the numerical simulations of the erater formation during impact of small accelerated object on bulk target. The simulation of the high-velocity impact problem by the Lagrangian hydrodynamical codes leads in later stages to severe distortion of the Lagrangian grid which prevents continuation of computation. Such situations can however be treated by the Arbitrary Lagrangian Eulerian (ALE) method. In order to maintain the grid quality, the ALE method applies grid smoothing regularly after several time steps of Lagrangian computation. After changing the grid, the conservative quantities have to be conservatively remapped from the old grid to the new, better one. After remapping, Lagrangian computation can continue.