Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows

Barlow, Andrew; Maire, Pierre‐Henri; Rider, William J.; Rieben, Robert N.; Shashkov, Mikhail

doi:10.1016/j.jcp.2016.07.001

Cited by 158 publications

(91 citation statements)

References 131 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a recently growing technique for modelling processes in which the Lagrangian and the Eulerian methods are combined into a single numerical approach called the Arbitrary Lagrangian Eulerian (ALE) [76]. In this approach, a user specifies a set of metrics that informs the analysis code in order to use the Lagrangian or the Eulerian.…”

Section: Different Welding Zones and Different Modelling Scalesmentioning

confidence: 99%

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

Meyghani

Awang

Emamian

et al. 2017

Metals

View full text Add to dashboard Cite

Friction Stir Welding (FSW) is a novel kind of welding for joining metals that are impossible or difficult to weld by conventional methods. Three-dimensional nature of FSW makes the experimental investigation more complex. Moreover, experimental observations are often costly and time consuming, and usually there is an inaccuracy in measuring the data during experimental tests. Thus, Finite Element Methods (FEMs) has been employed to overcome the complexity, to increase the accuracy and also to reduce costs. It should be noted that, due to the presence of large deformations of the material during FSW, strong distortions of mesh might be happened in the numerical simulation. Therefore, one of the most significant considerations during the process simulation is the selection of the best numerical approach. It must be mentioned that; the numerical approach selection determines the relationship between the finite grid (mesh) and deforming continuum of computing zones. Also, numerical approach determines the ability of the model to overcome large distortions of mesh and provides an accurate resolution of boundaries and interfaces. There are different descriptions for the algorithms of continuum mechanics include Lagrangian and Eulerian. Moreover, by combining the above-mentioned methods, an Arbitrary Lagrangian-Eulerian (ALE) approach is proposed. In this paper, a comparison between different numerical approaches for thermal analysis of FSW at both local and global scales is reviewed and the applications of each method in the FSW process is discussed in detail. Observations showed that, Lagrangian method is usually used for modelling thermal behavior in the whole structure area, while Eulerian approach is seldom employed for modelling of the thermal behavior, and it is usually employed for modelling the material flow. Additionally, for modelling of the heat affected zone, ALE approach is found to be as an appropriate approach. Finally, several significant challenges and subjects remain to be addressed about FSW thermal analysis and opportunities for the future work are proposed.

show abstract

Section: Different Welding Zones and Different Modelling Scalesmentioning

confidence: 99%

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

Meyghani

Awang

Emamian

et al. 2017

Metals

View full text Add to dashboard Cite

show abstract

“…In this second approach, the complex domain is embedded into a larger, regular domain and the boundary conditions are approximated by a variety of different techniques. Examples include the adaptive fast multipole accelerated Poisson solver (e.g., [4]), which combines boundary and volume integral methods in the larger domain, fictitious domain methods (e.g., [5,6,7,8]) where Lagrange multipliers are applied in order to enforce the boundary conditions, immersed boundary (e.g., [9,10,11,12]), front-tracking (e.g., [13,14,15]) and arbitrary Lagrangian-Eulerian methods (e.g., [16,17,18,19]) utilize separate surface and volume meshes where force distributions are interpolated from the surface to the volume meshes, in a neighborhood of the domain boundary, to approximate the boundary conditions. In addition, a number of specialized methods have been designed to achieve better than first order accuracy in the L ∞ norm.…”

Section: Introductionmentioning

confidence: 99%

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

Guo

Lowengrub

2020

Journal of Computational Physics

View full text Add to dashboard Cite

The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a larger, regular domain. The original PDE is reformulated using a smoothed characteristic function of the complex domain and source terms are introduced to approximate the boundary conditions. The reformulated equation, which is independent of the dimension and domain geometry, can be solved by standard numerical methods and the same solver can be used for any domain geometry. A challenge is making the method higher-order accurate. For Dirichlet boundary conditions, which we focus on here, current implementations demonstrate a wide range in their accuracy but generally the methods yield at best first order accuracy in , the parameter that characterizes the width of the region over which the characteristic function is smoothed. Typically, ∝ h, the grid size. Here, we analyze the diffuse-domain PDEs using matched asymptotic expansions and explain the observed behaviors. Our analysis also identifies simple modifications to the diffuse-domain PDEs that yield higher-order accuracy in , e.g., O( 2 ) in the L 2 norm and O( p ) with 1.5 ≤ p ≤ 2 in the L ∞ norm. Our analytic results are confirmed numerically in stationary and moving domains where the level set method is used to capture the dynamics of the domain boundary and to construct the smoothed characteristic function.

show abstract

“…In typical Lagrange-plus-remap ALE methods, [2][3][4][5] the mesh moves with the fluid in the Lagrangian step and is then smoothed in a way that improves mesh quality. In typical Lagrange-plus-remap ALE methods, [2][3][4][5] the mesh moves with the fluid in the Lagrangian step and is then smoothed in a way that improves mesh quality.…”

Section: Introductionmentioning

confidence: 99%

“…Arbitrary Lagrangian-Eulerian (ALE) solution algorithms 1 require some means by which the motion of the computational mesh is specified. In typical Lagrange-plus-remap ALE methods, [2][3][4][5] the mesh moves with the fluid in the Lagrangian step and is then smoothed in a way that improves mesh quality. A remapping or advection algorithm is used to transfer the solution from the post-Lagrangian mesh to the smoothed mesh.…”

Section: Introductionmentioning

confidence: 99%

Improved ALE mesh velocities for complex flows

Bakosi

Waltz

Morgan

2017

Numerical Methods in Fluids

View full text Add to dashboard Cite

Summary A key choice in the development of arbitrary Lagrangian‐Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring‐force model. This approach allows distinct and separate control over rotational and translational modes. The utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

show abstract

Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows

Cited by 158 publications

References 131 publications

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

Improved ALE mesh velocities for complex flows

Contact Info

Product

Resources

About