Three-dimensional numerical simulation of material mixing observed in FSW using a mesh-free approach

Mesmoudi, Said; Braikat, Bouazza; Lahmam, Hassane; Zahrouni, Hamid

doi:10.1007/s00366-018-0683-6

Cited by 19 publications

(13 citation statements)

References 24 publications

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“…is a quadratic form, which represents the convection term; and F is a given force vector. In the following section, we present the description of the HO‐MFA to solve problem . We show that this HO‐MFA is a powerful continuation method, which can be applied without correction.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In other works, the high‐order mesh‐free approach (HO‐MFA) is used for the computation of elasto‐plastic contact problems, the treatment of the frictional contact of two elastic deformable bodies in the static case, and buckling and postbuckling analysis of shells. In another hand, this algorithm is used for the simulation of material mixing observed in friction stir welding (FSW) process in dynamic case …”

Section: Introductionmentioning

confidence: 99%

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Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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Summary In this paper, we propose for the first time to extend the application field of the high‐order mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This approach is based on a high‐order algorithm, which combines a Taylor series expansion, a continuation technique, and a moving least squares (MLS) method. The Taylor series expansion permits to transform the nonlinear problem into a succession of continuous linear ones with the same tangent operator. The MLS method is used to transform the succession of continuous linear problems into discrete ones. The continuation technique allows to compute step‐by‐step the whole solution of the discrete problems. This mesh‐free approach is tested on three examples: a flow around a cylindrical obstacle, a flow in a sudden expansion, and the standard benchmark lid‐driven cavity flow. A comparison of the obtained results with those computed by the Newton‐Raphson method with MLS, the high‐order continuation with finite element method, and those of literature is presented.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, for solving the nonlinear unsteady problem (1), we apply the temporal implicit Euler scheme widely used in the resolution of transient problems [21,23,27] as…”

Section: Temporal Implicit Euler Schemementioning

confidence: 99%

“…The parameter a should be greater than or equal to one for computing solution (11). The validity range a max is described in [16,23,27,39] as…”

Section: High-order Continuation With Homotopy Transformationmentioning

confidence: 99%

“…Based on the FEM, many applications of high-order continuation (HOC) coupled with homotopy transformation show the performance of this technique with respect to computation time, automatic adaptability of the step length, and the exactness of solutions in structural and fluid mechanics [16][17][18][19]. In addition, the meshless method such as MLS approximation is coupled with HOC for the resolution of dynamic or static nonlinear problems [20][21][22][23][24][25][26][27][28]. Meshless methods such as MLS approximation have some difficulties in the treatment of essential boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Mesmoudi¹,

Askour²,

Braikat³

2020

Comptes Rendus. Mécanique

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Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

Rammane

Mesmoudi

Tri

et al. 2020

Numerical Methods in Fluids

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In this article, we propose to investigate numerically the steady bifurcation points and bifurcated branches in fluid mechanics by employing high‐order mesh‐free geometric progression algorithms. These algorithms are based on the use of the geometric progression (GP) in a high‐order mesh‐free approach. The first proposed algorithm is applied on a strong formulation using the moving least squares (MLS) approximation coupled with GP (HO‐MLS‐GPM). While the second proposed algorithm is applied on a weak formulation using the element‐free Galerkin (EFG) coupled also with GP (HO‐EFG‐GPM). The incompressibility condition is taken by introducing the penalty technique to transform the stationary Navier–Stokes equations verified by the pressure and velocity into ones verified by only the velocity. The high‐order mesh‐free algorithm permits to transform this nonlinear equations into a succession of linear ones. The GP allows to detect with precision the bifurcation points and the Lyapunov–Schmidt reduction is coupled with HO‐MLS‐GPM and HO‐EFG‐GPM as a continuation procedure to follow the many bifurcated branches. The aim of this resolution strategy concerns the treatment of the bifurcation phenomena for a fluid flow through an expansion in several geometries, where the steady flow becomes unstable after a critical Reynolds value. The obtained results are compared with those presented in literature and with those computed using the high‐order finite element algorithm coupled with GP.

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Three-dimensional numerical simulation of material mixing observed in FSW using a mesh-free approach

Cited by 19 publications

References 24 publications

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

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