Mesh motion techniques for the ALE formulation in 3D large deformation problems

Aymone, José Luf́s Farinatti

doi:10.1002/nme.939

Cited by 19 publications

(5 citation statements)

References 34 publications

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“…The method proposed by Aymone [45] is similar to the arc method: a quadratic interpolation is built through a given node of the sharp edge and its two direct neighbours. The node is relocated to the curvilinear abscissa 2 OE 1, 1, which makes the adjacent element shapes more uniform.…”

Section: Alternative Methodsmentioning

confidence: 99%

“…Transfinite mapping [59] has been firstly used in the frame of the FEM by Haber [60]. In ALE formalism, it is commonly used in 2D [28,35,45,50,53,61,62]. In this work, it is used in either 2D or 3D.…”

Section: Direct Methodsmentioning

confidence: 99%

“…The corner nodes are located at the vertices of the computational domain. In solid mechanics, when the ALE formalism is used to avoid mesh distortions, the material should remain inside the mesh and the corner nodes must be Lagrangian, so no special treatment is needed (see [45] or [46], for example).…”

Section: Corner Nodes and Eulerian Boundariesmentioning

confidence: 99%

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Efficient ALE mesh management for 3D quasi‐Eulerian problems

Boman

Ponthot

2012

Numerical Meth Engineering

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SUMMARY In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi‐Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU‐efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16‐stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Alternative Methodsmentioning

confidence: 99%

Section: Direct Methodsmentioning

confidence: 99%

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Efficient ALE mesh management for 3D quasi‐Eulerian problems

Boman

Ponthot

2012

Numerical Meth Engineering

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“…In Problem 3 or 4, respectively, the stabilized discrete form A s h , that is defined in (16) along with ( 11) and ( 2), evokes the computation of integrals over the fluid domain. Due to the usage of unfitted meshes, integrals over the portions of the cut cells, that are filled with fluid, have thus to be evaluated.…”

Section: Integration Over Cut Cellsmentioning

confidence: 99%

“…In classical ALE approaches, larger motions and deformations of the domains lead to a poor quality of the non-transformed, physical mesh (cf., e.g. [14,15,16]), since the computational mesh has to track and resolve moving boundaries or interfaces. This mesh deformation impacts the transformation of the model equations to the reference domain and, thereby, the stability of the overall ALE approach.…”

Section: Introductionmentioning

confidence: 99%

Cut finite element methods and ghost stabilization techniques for space‐time discretizations of the Navier–Stokes equations

Anselmann

Bause

2022

Numerical Methods in Fluids

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We propose and analyze numerically a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The physical domain is embedded into a fixed computational mesh such that arbitrary intersections of the moving domain's boundaries with the background mesh occur. The key ingredients of the approach are the weak formulation of Dirichlet boundary conditions by Nitsche's method, the flexible and efficient integration over all types of intersections of cells by moving boundaries and the spatial extension of the discrete physical quantities to the entire computational background mesh including fictitious (ghost) subdomains of fluid flow. To prevent spurious oscillations caused by irregular intersections of mesh cells, a penalization ensuring the stability of the approach and defining implicitly the extension to host domains is added. These techniques are embedded in an arbitrary order, discontinuous Galerkin discretization of the time variable and an inf-sup stable discretization of the spatial variables. The convergence and stability properties of the approach are studied, firstly, for a benchmark problem of flow around a stationary obstacle and, secondly, for flow around moving obstacles with arising cut cells and fictitious domains. The parallel implementation is also addressed.

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High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes

Gawlik

Kabaria

Lew

2015

Numerical Meth Engineering

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We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off-the-shelf time integrators. We demonstrate the approach by using Taylor-Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge-Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations.Organization. This paper is organized as follows. In Section 2, we recall the governing equations for incompressible, viscous flow around a moving obstacle with prescribed evolution, and we recast the equations in weak form. In Section 3, we propose a discretization of the aforementioned equations using a universal mesh in conjunction with Taylor-Hood finite elements [61]. To integrate in time, we propose the use of implicit Runge-Kutta schemes as well as a fractional step scheme. In Section 4, we apply the proposed methods to simulate flow around various obstacles with prescribed evolution: The setup we have described thus far offers the freedom to employ a time integrator of one's choosing to numerically integrate (17), a system of DAEs of index 2, from t D t n 1 to t D t n . We present two examples of integration schemes: a singly diagonally implicit Runge-Kutta (SDIRK) scheme [69,70] and a fractional step scheme [71][72][73]. In accordance with common guidelines for numerically solving DAEs, the SDIRK schemes we consider are stiffly accurate (and hence L-stable) methods [70,74]. The same schemes are considered by, for instance, [75,76] in their studies of high-order methods for the Navier-Stokes equations on fixed domains.We immersed the oscillating disk in a domain D D OE 6; 6 OE 3; 3 and prescribed boundary conditions ‡ In the case of the fractional step scheme, the error in p was measured at t D T t=2 rather than at t D T .

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Mesh motion techniques for the ALE formulation in 3D large deformation problems

Cited by 19 publications

References 34 publications

Efficient ALE mesh management for 3D quasi‐Eulerian problems

Efficient ALE mesh management for 3D quasi‐Eulerian problems

Cut finite element methods and ghost stabilization techniques for space‐time discretizations of the Navier–Stokes equations

High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes

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