An arbitrary Lagrangian-Eulerian framework with exact mass conservation for the numerical simulation of 2D rising bubble problem

2017 ◽  
Vol 112 (13) ◽  
pp. 2110-2134 ◽  
Author(s):  
Cagatay Guventurk ◽  
Mehmet Sahin
Keyword(s):  
Numerical Simulation ◽  
Mass Conservation ◽  
Arbitrary Lagrangian Eulerian ◽  
Exact Mass ◽  
Rising Bubble

Continuous Roll Forming Simulation Using Arbitrary Lagrangian Eulerian Formalism

2011 ◽  
Vol 473 ◽  
pp. 564-571 ◽  
Author(s):  
Romain Boman ◽  
Jean Philippe Ponthot
Keyword(s):  
Numerical Simulation ◽  
Rolling Direction ◽  
Initial Guess ◽  
Roll Forming ◽  
Arbitrary Lagrangian Eulerian ◽  
The Finite Element Method ◽  
Forming Simulation ◽  
Element Size ◽  
Cold Roll ◽  
Classical Lagrangian

Due to the length of the mill, accurate modelling of stationary solution of continuous cold roll forming by the finite element method using the classical Lagrangian formulation usually requires a very large mesh leading to huge CPU times. In order to model industrial forming lines including many tools in a reasonable time, the sheet has to be shortened or the element size has to be increased leading to inaccurate results. On top of this, applying loads and boundary conditions on this smaller sheet is usually more difficult than in the continuous case. Moreover, transient dynamic vibrations, which are unnecessarily computed, may appear when the sheet hits each tool, decreasing the convergence rate of the numerical simulation. Beside this classical Lagrangian approach, an alternative method is given by the Arbitrary Lagrangian Eulerian (ALE) formalism which consists in decoupling the motion of the material and the mesh. Starting from an initial guess of the sheet geometry between the rolls, the numerical simulation is performed until the stationary state is reached with a mesh, the nodes of which are fixed in the rolling direction but are free to move on perpendicular plane, following the geometrical boundary of the sheet. The whole forming line can then be modelled using a limited number of brick and contact elements because the mesh is only refined near the tools where bending and contact occur. In this paper, ALE results are compared to previous Lagrangian simulations and experimental measurement on a U-channel, including springback. Advantages of the ALE method are finally demonstrated by the simulation of a tubular rocker panel on a 16-stands forming mill.

scholarly journals A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

2014 ◽  
Vol 7 (3) ◽  
pp. 909-929 ◽  
Author(s):  
J. Thuburn ◽  
C. J. Cotter ◽  
T. Dubos
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Model Comparison ◽  
Mass Conservation ◽  
Time Discretization ◽  
Water Model ◽  
Tracer Transport ◽  
Exact Mass ◽  
Large Wave ◽  
Cubed Sphere

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Numerical Simulation of Flash Floods Routing Based on Improved Leap-Frog Method

2013 ◽  
Vol 347-350 ◽  
pp. 2173-2177
Author(s):  
Jia Hua Zhang ◽  
Chi Zhang
Keyword(s):  
Numerical Simulation ◽  
Moving Boundary ◽  
Simulation Analysis ◽  
Flash Flood ◽  
Mass Conservation ◽  
Correction Method ◽  
Gansu Province ◽  
Simulation Accuracy ◽  
Whole Process ◽  
Steep Terrain

in the 2-d numerical simulation of flash flood disaster, due to flood often occurred in the steep terrain and water flow rapidly changed, lead to that the calculated value is unstable and even the calculation diverge in the simulation. This paper presents a grid outflow correction method, which is based on the leap-frog finite difference format, through modifying the outflow rate of the grid circularly, to ensure the mass conservation in the whole process of computing. In the local dam bursting model, the simulated result comparison of the grid outflow correction method and the algorithm of implicit alternating direction on the mass conservation shows that, the new method can ensure the simulation accuracy and the numerical stability under the condition of steep terrain and moving boundary. According to the proposed method, the simulation analysis in the process of extreme flash flood disasters which happened in 2010 Zhouqu county in Gansu province was carried out. The comparison of simulation results and remote sensing estimation results shows that the deviation of the flood evolution time, speed and impact height are within 5%, and the consistency of evolution path is good, which verifies the validity of the algorithm.

Numerical Simulation of Friction Stir Welding (FSW) Process Based on ABAQUS Environment

2016 ◽  
Vol 254 ◽  
pp. 272-277
Author(s):  
Monica Iordache ◽  
Claudiu Bădulescu ◽  
Eduard Niţu ◽  
Doina Iacomi
Keyword(s):  
Numerical Simulation ◽  
Friction Stir Welding ◽  
Finite Elements ◽  
Adaptive Mesh ◽  
Experimental Tests ◽  
Arbitrary Lagrangian Eulerian ◽  
Complex Issue ◽  
Friction Stir ◽  
Mechanical Phenomena

. Simulation of the FSW process is a complex issue, as it implies interactions between thermal and mechanical phenomena and the quality of the welding depends on many factors. In order to reduce the time of the experimental tests, which can be long and expensive, numerical simulation of the FSW process has been tried during the last ten years. However, there still remain aspects that cannot be completely simulated. In this paper the authors present the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Arbitrary Lagrangian Eulerian (ALE) adaptive mesh controls.

Numerical Simulation of Polyurethane Pad Punching Process

2014 ◽  
Vol 941-944 ◽  
pp. 1817-1821
Author(s):  
Xiao Xiong Wang ◽  
Jing Liu ◽  
Jing Tao Han ◽  
Qian Liu
Keyword(s):  
Numerical Simulation ◽  
Cross Section ◽  
Shear Failure ◽  
Sheet Thickness ◽  
Control Parameters ◽  
Arbitrary Lagrangian Eulerian ◽  
Adaptive Meshing ◽  
Finite Element Program ◽  
Element Program ◽  
Punching Process

A numerical simulation was conducted to investigate the effect of the punching clearance, the thickness of sheet, and the hardness of polyurethane pad on the process of punching by finite element program ABAQUS which based on shear failure criterion and arbitrary Lagrangian-Eulerian adaptive meshing method. And the collapse height dimension and width dimension tendency of the sheet under different control parameters was analyzed after punching process according to this simulation result. The results show that the collapse height dimension and width dimension decreased with the increase of the polyurethane hardness, it means the cross section quality perspicuously has been increased; the collapse height dimension and width dimension decreased with the increasing of the sheet thickness; while the influence of the punching gap is indistinctive.

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