The CIP method embedded in finite element discretizations of incompressible fluid flows

Banijamali, Bahareh; Bathe, Klaus‐Jürgen

doi:10.1002/nme.1942

Cited by 13 publications

(6 citation statements)

References 17 publications

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“…This means in essence to construct special interpolation functions that are more amenable to capture the desired response. This approach is rather natural to increase the effectiveness of the finite element method for the solution of specific problems, and has been pursued for a long time, like for example in the analysis of wave propagations [67][68][69], global local solutions [70,71], piping analyses [72], the development of beam elements [73], and in fluid flow analyses [74,75]. Such methods have lately also been referred to as partition of unity methods or extended finite element methods, see for example [76][77][78][79].…”

Section: Nonlinear Sheath-plasma Interactions In 2d Slab Geometrymentioning

confidence: 99%

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

2012

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Electromagnetic plasma waves in the ion cyclotron range of frequencies (ICRF) are routinely used in magnetic fusion experiments to heat plasmas and drive currents. However, many experiments have revealed that wave energy losses in the plasma edge and at the wall are significant, and detected that the acceleration of ions into the walls due to the formation of radio-frequency (RF) sheaths is one of the root causes of this problem. Since the RF-enhanced sheaths have many undesirable effects, such as impurity production and hot spot generation, a predictive numerical tool is required to quantitatively evaluate these effects with complicated boundary shapes of tokamaks taken into account.In this thesis the numerical code that solves self-consistent RF sheath-plasma interactions in the scrape-off layer for ICRF heating is developed based on a nonlinear finite element technique and is applied to various problems in the one-dimensional (1D) and two-dimensional (2D) domains corresponding to simplified models for the poloidal plane of a tokamak. The present code solves for plasma waves based on the cold plasma model subject to the sheath boundary condition, in which the most important physics that happens in the sheath is captured without using the field quantities in the sheath.Using the developed finite element code, several new properties of the RF sheathplasma interactions are discovered. First, it is found in the 1D domain that multiple roots can be present due to the resonance of the propagating slow wave and its nonlinear interaction with the sheath. Second, sheath-plasma waves are identified in a 2D slab geometry, and it is proved in conjunction with an electrostatic 2D sheath mode analysis that the sheath-plasma wave only appears in the vicinity of the sheath surface if the plasma density is greater than the lower hybrid density, and its wavelength depends on various parameters. Third, as a consequence of the selfconsistent interaction between the propagating slow wave and the sheath, it is shown that the electric field distribution pattern in the plasma smoothly varies along the magnetic field lines between the conducting-wall and quasi-insulating limits.In the numerical analysis employing the 2D domain whose scale is equivalent to the Alcator C-Mod device, it is demonstrated that the calculated sheath potential can reach the order of kV, which is sufficient to yield enhanced sputtering at the wall. In addition, it is shown that the sheath potential in the close vicinity of the antenna current strap can be insensitive to the direction of the background magnetic field in the RF sheath dominated regime. Further, it is found from a series of nonlinear calculations that the sheath potential sensitively varies depending on the plasma density and electron temperature, which is consistent with the scaling derived from the Child-Langmuir law and the definition of the RF sheath potential.Lastly, a new finite element approach, which is named the finite element wavepacket method, is developed for the purpose of so...

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Section: Nonlinear Sheath-plasma Interactions In 2d Slab Geometrymentioning

confidence: 99%

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

2012

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“…The IRBFN-based methods have been shown in [29] to have definite advantage in terms of accuracy and stability owing to its ability to ensure C p solutions, where p is the order of the governing PDEs, across subdomain interfaces. In order to achieve highly-stable numerical schemes for the simulation of viscous flows at high Reynolds numbers such as those reported by Bathe and co-workers [30][31][32], further studies are needed.…”

Section: Comparison With Principal Discretisation Techniquesmentioning

confidence: 99%

Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

Mai‐Duy¹,

Tran-Cong²

2009

Computers & Structures

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“…These elements result in much more accurate solutions in linear and nonlinear analyses. The same approach has been used, for example, in the development of beam elements to include warping effects [48], in fluid flow analyses to better capture the flow conditions [49,50], and in solid mechanics to predict locally nonsmooth features like needed for cracks, voids and failure [51,52]. In each of these cases, in essence, the 'character' of the solution sought is embedded in the solution space.…”

Section: Introductionmentioning

confidence: 99%

A finite element method enriched for wave propagation problems

Ham

Bathe

2012

Computers & Structures

Self Cite

172

110

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An enriched finite element method is presented to solve various wave propagation problems. The proposed method is an extension of the procedure introduced by Kohno, Bathe, and Wright for one-dimensional problems [1]. Specifically, the novelties are: two-dimensional problems are solved (and three-dimensional problems would be tackled similarly), a scheme is given to overcome ill-conditioning, the method is presented for time-dependent problems, and focus is on the solution of problems in solids and structures using real arithmetic only. The method combines advantages of finite element and spectral techniques, but an important point is that it preserves the fundamental properties of the finite element method. The general formulation of the procedure is given and various examples are solved to illustrate the capabilities of the proposed scheme.

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The CIP method embedded in finite element discretizations of incompressible fluid flows

Cited by 13 publications

References 17 publications

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

A finite element method enriched for wave propagation problems

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