scholarly journals Asymptotic Shallow Models Arising in Magnetohydrodynamics

Water Waves ◽  
2021 ◽  
Author(s):  
Diego Alonso-Orán

AbstractIn this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, we present the magnetic analogue of the 2D Green–Naghdi equations for water waves under a weak magnetic pressure assumption in the presence of weakly sheared vorticity and magnetic currents. Our method is inspired by ideas for hydrodynamic flows developed in Castro and Lannes (2014) to reduce the three-dimensional dynamics of the vorticity and current to a finite cascade of two dimensional equations which can be closed at the precision of the model.

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.


Geosciences ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 76
Author(s):  
Ashraf Hefny ◽  
Mohamed Ezzat Al-Atroush ◽  
Mai Abualkhair ◽  
Mariam Juma Alnuaimi

The complexities and the economic computational infeasibility associated in some cases, with three-dimensional finite element models, has imposed a motive for many investigators to accept numerical modeling simplification solutions such as assuming two-dimensional (2D) plane strain conditions in simulation of several supported-deep excavation problems, especially for cases with a relatively high aspect ratio in plan dimensions. In this research, a two-dimensional finite element model was established to simulate the behavior of the supporting system of a large-scale deep excavation utilized in the construction of an underground metro station Rod El Farrag project (Egypt). The essential geotechnical engineering properties of soil layers were calculated using results of in-situ and laboratory tests and empirical correlations with SPT-N values. On the other hand, a three-dimensional finite element model was established with the same parameters adopted in the two-dimensional model. Sufficient sensitivity numerical analyses were performed to make the three-dimensional finite element model economically feasible. Results of the two-dimensional model were compared with those obtained from the field measurements and the three-dimensional numerical model. The comparison results showed that 3D high stiffening at the primary walls’ corners and also at the locations of cross walls has a significant effect on both the lateral wall deformations and the neighboring soil vertical settlement.


2013 ◽  
Vol 27 (6) ◽  
pp. 2915-2922 ◽  
Author(s):  
Yesica E. Alvarez ◽  
Brian M. Moreno ◽  
Michael T. Klein ◽  
Justin K. Watson ◽  
Fidel Castro-Marcano ◽  
...  

Author(s):  
Gillian Leplat ◽  
Emmanuel Laroche ◽  
Philippe Reulet ◽  
Pierre Millan

A two-dimensional numerical analysis of a laminar natural convection flow within an air-filled enclosure is proposed in this paper from an unstable configuration previously studied experimentally. The flow is driven by a heated square-section cylinder located at the center of a square-section enclosure. Instabilities are observed for an aspect ratio (height of the cylinder over the height of the cavity) of 0.4 and cause the flow to turn into a three-dimensional and unsteady regime characterized by a symmetry breaking and large scale high amplitude flappings around the cylinder. The multi-physic computational software CEDRE, developed at the ONERA, is used to study this unstable behavior and a time-dependent compressible flow solver is used to perform the two-dimensional simulations under the low Mach number approximation, corresponding to the mid-depth cross-section of the enclosure from the experimental configuration. The first results on the investigation of the first unstable modes confirm the onset of the instabilities at the Rayleigh number of the experiment with asymmetrical motions of the fluid around the cylinder. Further analyses highlight the critical Rayleigh number that defines the instability threshold of the first bifurcation which origin and nature could have been identified. Finally, joint fluid-solid simulations are performed to determine more precisely the role of boundary conditions in the onset of instabilities.


2021 ◽  
Author(s):  
Ray Chapman ◽  
Phu Luong ◽  
Sung-Chan Kim ◽  
Earl Hayter

The Environmental Laboratory (EL) and the Coastal and Hydraulics Laboratory (CHL) have jointly completed a number of large-scale hydrodynamic, sediment and water quality transport studies. EL and CHL have successfully executed these studies utilizing the Geophysical Scale Transport Modeling System (GSMB). The model framework of GSMB is composed of multiple process models as shown in Figure 1. Figure 1 shows that the United States Army Corps of Engineers (USACE) accepted wave, hydrodynamic, sediment and water quality transport models are directly and indirectly linked within the GSMB framework. The components of GSMB are the two-dimensional (2D) deep-water wave action model (WAM) (Komen et al. 1994, Jensen et al. 2012), data from meteorological model (MET) (e.g., Saha et al. 2010 - http://journals.ametsoc.org/doi/pdf/10.1175/2010BAMS3001.1), shallow water wave models (STWAVE) (Smith et al. 1999), Coastal Modeling System wave (CMS-WAVE) (Lin et al. 2008), the large-scale, unstructured two-dimensional Advanced Circulation (2D ADCIRC) hydrodynamic model (http://www.adcirc.org), and the regional scale models, Curvilinear Hydrodynamics in three dimensions-Multi-Block (CH3D-MB) (Luong and Chapman 2009), which is the multi-block (MB) version of Curvilinear Hydrodynamics in three-dimensions-Waterways Experiments Station (CH3D-WES) (Chapman et al. 1996, Chapman et al. 2009), MB CH3D-SEDZLJ sediment transport model (Hayter et al. 2012), and CE-QUAL Management - ICM water quality model (Bunch et al. 2003, Cerco and Cole 1994). Task 1 of the DOER project, “Modeling Transport in Wetting/Drying and Vegetated Regions,” is to implement and test three-dimensional (3D) wetting and drying (W/D) within GSMB. This technical note describes the methods and results of Task 1. The original W/D routines were restricted to a single vertical layer or depth-averaged simulations. In order to retain the required 3D or multi-layer capability of MB-CH3D, a multi-block version with variable block layers was developed (Chapman and Luong 2009). This approach requires a combination of grid decomposition, MB, and Message Passing Interface (MPI) communication (Snir et al. 1998). The MB single layer W/D has demonstrated itself as an effective tool in hyper-tide environments, such as Cook Inlet, Alaska (Hayter et al. 2012). The code modifications, implementation, and testing of a fully 3D W/D are described in the following sections of this technical note.


2021 ◽  
Author(s):  
Jianming Cai ◽  
Han Bao ◽  
Quan Xu ◽  
Zhongyun Hua ◽  
Bocheng Bao

Abstract The Hindmarsh-Rose (HR) neuron model is built to describe the neuron electrical activities. Due to the polynomial nonlinearities, multipliers are required to implement the HR neuron model in analog. In order to avoid the multipliers, this brief presents a novel smooth nonlinear fitting scheme. We first construct two nonlinear fitting functions using the composite hyperbolic tangent functions and then implement an analog multiplierless circuit for the two-dimensional (2D) or three- dimensional (3D) HR neuron model. To exhibit the nonlinear fitting effects, numerical simulations and hardware experiments for the fitted HR neuron model are provided successively. The results show that the fitted HR neuron model with analog multiplierless circuit can display different operation patterns of resting, periodic spiking, and periodic/chaotic bursting, entirely behaving like the original HR neuron model. The analog multiplierless circuit has the advantage of low implementation cost and thereby it might be suitable for the hardware implementation of large-scale neural networks.


2020 ◽  
Vol 494 (2) ◽  
pp. 1826-1837 ◽  
Author(s):  
A de Lorenzo-Cáceres ◽  
J Méndez-Abreu ◽  
B Thorne ◽  
L Costantin

ABSTRACT The intrinsic photometric properties of inner and outer stellar bars within 17 double-barred galaxies are thoroughly studied through a photometric analysis consisting of (i) two-dimensional (2D) multicomponent photometric decompositions, and (ii) three-dimensional (3D) statistical deprojections for measuring the thickening of bars, thus retrieving their 3D shape. The results are compared with previous measurements obtained with the widely used analysis of integrated light. Large-scale bars in single- and double-barred systems show similar sizes, and inner bars may be longer than outer bars in different galaxies. We find two distinct groups of inner bars attending to their in-plane length and ellipticity, resulting in a bimodal behaviour for the inner/outer bar length ratio. Such bimodality is related neither to the properties of the host galaxy nor the dominant bulge, and it does not show a counterpart in the dimension off the disc plane. The group of long inner bars lays at the lower end of the outer bar length versus ellipticity correlation, whereas the short inner bars are out of that relation. We suggest that this behaviour could be due to either a different nature of the inner discs from which the inner bars are dynamically formed or a different assembly stage for the inner bars. This last possibility would imply that the dynamical assembly of inner bars is a slow process taking several Gyr to happen. We have also explored whether all large-scale bars are prone to develop an inner bar at some stage of their lives, possibility we cannot fully confirm or discard.


1996 ◽  
Vol 12 (04) ◽  
pp. 269-275
Author(s):  
Panagiotis Michaleris ◽  
Andrew DeBiccari

This paper presents an efficient and effective numerical analysis technique for predicting welding-induced buckling. The technique combines three-dimensional structural analyses with two-dimensional welding simulations. Implementation of the technique can determine the appropriate welding conditions under which the design critical buckling load is not exceeded. Experimental results obtained from small-and large-scale mock-up panels are used to confirm the predictions of the analytical models, The paper concludes with a study of the effects of heat input (weld size), panel size, and panel thickness on buckling distortion.


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