On the role and value of <i>β</i> in incompressible MHD simulations

Chahine, Robert; Bos, Wouter J. T.

doi:10.1063/1.5018666

Cited by 5 publications

(6 citation statements)

References 29 publications

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“…The size of the temporal fluctuations of the different quantities around the time-averaged value are indicated by error bars. In agreement with the results of Chahine & Bos (2018), the value of is decreasing for increasing values of the Lundquist number. We see that for the highest values of , has dropped most importantly in the circular geometry.…”

Section: Resultssupporting

confidence: 91%

“…It is known from turbulence research that estimating simply the order of magnitude of pressure gradients by , with a macroscopic lengthscale, can seriously underestimate their magnitude because the pressure gradients are, in general, dominated by small-scale contributions . Therefore, we recently introduced the alternative, gradient-based s (Chahine & Bos 2018), It is only when is small compared to unity that the influence of the pressure term might be negligible in the dynamics, compared with the influence of the other terms in the velocity equation. This is not necessarily the case when is small.…”

Section: Resultsmentioning

confidence: 99%

“…Indeed, in some recent RFP investigations, the pressure is retained (Mizuguchi et al. 2012) and recently we focused on the importance of the pressure dynamics (Chahine & Bos 2018). In particular, we illustrated in MHD simulations in cylindrical geometry that, to understand the dynamics of the plasma, the important quantity to monitor is not the pressure but its gradient.…”

Section: Equations Numerical Methods and Parametersmentioning

confidence: 99%

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Effect of shaping on turbulent dynamics in reversed-field pinch simulations

2021

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We study the influence of the shape of the plasma container on the dynamics of the reversed-field pinch (RFP). The geometries we consider are periodic cylinders with elliptical and circular-shaped cross-sections. Numerical simulations of fully nonlinear viscoresistive magnetohydrodynamics are carried out to illustrate how the plasma dynamics is affected by shaping. It is shown that independent of the plasma shape, the quantity $\beta$ , comparing the hydrodynamic pressure to the magnetic pressure, decreases for increasing values of the Lundquist number, but the pressure gradient fluctuations remain roughly constant, when compared to the Lorentz force. Different elliptical shapes of the cross-section of the domain lead to the excitation of different toroidal (or axial) magnetic and dynamic modes. Furthermore, it is found that in a geometry with circular cross-section, a significant local poloidal angular momentum is observed, absent in the geometries with elliptical cross-section. Because the confinement is dominantly determined by plasma movement, and the dynamics of the velocity and magnetic field are modified by the modification of the geometry, shaping can thus affect the performance of RFP devices.

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Section: Resultssupporting

confidence: 91%

Section: Resultsmentioning

confidence: 99%

Section: Equations Numerical Methods and Parametersmentioning

confidence: 99%

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Effect of shaping on turbulent dynamics in reversed-field pinch simulations

2021

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“…In the present simulations the resolution is 64 × 64 × 512 grid-points in the x, y, z-directions, respectively. The pressure is computed from the resolution of the Poisson equation in the spectral domain 33 The initial magnetic field is a combination of an axial field This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

Section: A Mhd Simulations Of the Rfp Magnetic And Velocity Fieldsmentioning

confidence: 99%

The dynamo properties of the reversed field pinch velocity field

2022

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Reversed field pinch (RFP) is a toroidal device aiming at magnetic confinement of a plasma in order to reach conditions of thermonuclear reactions. In RFPs, the magnetic and velocity fields self-organize to a saturated state determined by their nonlinear interplay and the values of the transport-coefficients. The question addressed in this article is whether this saturated velocity field is capable of amplifying a seed magnetic field, the so-called dynamo-effect for the astrophysical community. It is shown, using numerical simulations in periodic cylinders, that the RFP velocity field can amplify a passively advected seed-field, but this is only observed for values of the magnetic Prandtl number above unity. These observations are reported for both laminar and turbulent RFP flows. We further assess the difference in behavior between a passively advected vector field and the true magnetic field and show that their difference is associated with the detailed alignment properties of the fields.

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“…where max t denotes the maximum value of the desired quantity over the considered time range, j max,PS , j max,BGK , j max,S and j max,SS are the time-dependent peak values of the density of the electric current obtained by the pseudo-spectral analysis 61 , the BGK LBM, the simplified lattice Boltzmann method and the present scheme, respectively. From this table, it is possible to appreciate that the error obtained by the present method is about seven times lower than the one made by the classical two-steps simplified approach.…”

Section: B Three-dimensional Simulationsmentioning

confidence: 99%

One-stage simplified lattice Boltzmann method for two- and three-dimensional magnetohydrodynamic flows

Rosis

Revell

2021

Physics of Fluids

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In this paper, we propose a new simplified lattice Boltzmann method (SLBM) for magnetohydrodynamic flows that outperforms the classical one in terms of accuracy, while preserving its advantages. A very recent paper [A. De Rosis, J. Al-Adham, H. Al-Ali and R. Meng, "Double-D2Q9 lattice Boltzmann models with extended equilibrium for two-dimensional magnetohydrodynamic flows", Phys. Fluids 33, 035143 (2021)] demonstrated that the SLBM enforces the divergence-free condition of the magnetic fiield in an excellent manner and involves the lowest amount of virtual memory. However, the SLBM is characterised by the poorest accuracy. Here, the two-stages algorithm that is typical of the SLBM is replaced by a one-stage procedure following the approach devised for non-conductive fluids in a very recent effort [A. Delgado-Gutierrez, P. Marzocca, D. Cardenas, and O. Probst, "A single-step and simplified graphics processing unit lattice Boltzmann method for high turbulent flows", International Journal for Numerical Methods in Fluids ( 2021)]. The Chapman-Enskog expansion formally demonstrates the consistency of the present scheme. The resultant algorithm is very compact and easy to be implemented. Given all these features, we believe that the proposed approach is an excellent candidate to perform numerical simulations of two-and three-dimensional magnetohydrodynamic flows.

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On the role and value of β in incompressible MHD simulations

Cited by 5 publications

References 29 publications

Effect of shaping on turbulent dynamics in reversed-field pinch simulations

Effect of shaping on turbulent dynamics in reversed-field pinch simulations

The dynamo properties of the reversed field pinch velocity field

One-stage simplified lattice Boltzmann method for two- and three-dimensional magnetohydrodynamic flows

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