A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system

Ni, Ming-Jiu; Munipalli, Ramakanth; Morley, Neil B.; Huang, Peter; Abdou, Mohamed

doi:10.1016/j.jcp.2007.07.025

Cited by 224 publications

(156 citation statements)

References 36 publications

(65 reference statements)

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“…As a numerical method, we apply the finite difference scheme described by Krasnov, Zikanov & Boeck (2011a). The scheme is based on the conservative discretization of Morinishi et al (1998) extended to the case of MHD flows by Ni et al (2007). We have found that the scheme is capable of accurate and numerically stable simulations of flows at high Hartmann number.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

2012

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High-resolution direct numerical simulations are conducted to analyse turbulent states of the flow of an electrically conducting fluid in a duct of square cross-section with electrically insulating walls and imposed transverse magnetic field. The Reynolds number of the flow is 10 5 and the Hartmann number varies from 0 to 400. It is found that there is a broad range of Hartmann numbers in which the flow is neither laminar nor fully turbulent, but has laminar core, Hartmann boundary layers and turbulent zones near the walls parallel to the magnetic field. Analysis of turbulent fluctuations shows that each zone consists of two layers: the boundary layer near the wall characterized by small-scale turbulence and the outer layer dominated by large-scale vortical structures strongly elongated in the direction of the magnetic field. We also find a peculiar scaling of the mean velocity, according to which the reciprocal von Kármán coefficient grows nearly linearly with the distance to the wall.

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Section: Introductionmentioning

confidence: 99%

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

2012

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“…The computations progressed quickly over the next three decades reaching Hartmann numbers on the order of hundreds in the late 1980s (e.g., [4]) and a few thousands recently [5]. Significant acceleration in MHD computations can be seen at around 2005 due to development of a new consistent and conservative scheme [6]. However, the progress has been different between simple geometry flows (e.g.…”

Section: Mhd Modeling Backgroundmentioning

confidence: 99%

An approach to verification and validation of MHD codes for fusion applications

Smolentsev

Badia

Bhattacharyay

et al. 2015

Fusion Engineering and Design

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We propose a new activity on verification and validation (V&V) of MHD codes presently employed by the fusion community as a predictive capability tool for liquid metal cooling applications, such as liquid metal blankets. The important steps in the development of MHD codes starting from the 1970s are outlined first and then basic MHD codes, which are currently in use by designers of liquid breeder blankets, are reviewed. A benchmark database of five problems has been proposed to cover a wide range of MHD flows from laminar fully developed to turbulent flows, which are of interest for fusion applications: (A) 2D fully developed laminar steady MHD flow, (B) 3D laminar, steady developing MHD flow in a non-uniform magnetic field, (C) quasitwo-dimensional MHD turbulent flow, (D) 3D turbulent MHD flow, and (E) MHD flow with heat transfer (buoyant convection). Finally, we introduce important details of the proposed activities, such as basic V&V rules and schedule. The main goal of the present paper is to help in establishing an efficient V&V framework and to initiate benchmarking among interested parties. The comparison results computed by the codes against analytical solutions and trusted experimental and numerical data as well as code-to-code comparisons will be presented and analyzed in companion paper/papers.

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“…The realization of the apply blk vector by the BlkOp class just performs the operation y := Ax, where x, y are instances of the Blk vector class. On the other hand, the BlkPrecondLU represents an approximate block LU factorization (see P (A) in (30)). 3 Its realization of the apply blk vector performs the operation "Solve (LU )y = r", where L and U are lower and upper block triangular factors, respectively, built from nblk × nblk Operators each, and r, y are Blk vector instances.…”

Section: Software Design and Implementationmentioning

confidence: 99%

“…The most particular feature of our approach is the explicit introduction of the current density as an additional unknown of the problem. We note that the typical approach is to decouple fluid and electromagnetic problems [12,28,31,30]. Then, the electromagnetic problem is solved in terms of the electric potential only and the current density and Lorentz force are computed.…”

Section: Introductionmentioning

confidence: 99%

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

Badia

Martı́n

Planas

2014

Journal of Computational Physics

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The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider a LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknown, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

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A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system

Cited by 224 publications

References 36 publications

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

An approach to verification and validation of MHD codes for fusion applications

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

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