A discontinuous Galerkin method for the full two-fluid plasma model

Loverich, John; Shumlak, U.

doi:10.1016/j.cpc.2005.03.058

Cited by 37 publications

(27 citation statements)

References 16 publications

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“…[2] Solutions are found with up to 16 th order spatial accuracy and 3 rd order temporal accuracy. [7] The multi-fluid plasma algorithm is used to model multiscale physics of current-carrying plasmas, such as the Z-pinch [4] and the field reversed configuration (FRC) [5].…”

Section: Executive Summarymentioning

confidence: 99%

“…The evolution of the reconnected magnetic flux compares remarkably well with the published data. [2] Additional applications are discussed in more detail below.…”

Section: High-order Discontinuous Galerkin Methodsmentioning

confidence: 99%

“…We have developed a discontinuous Galerkin method [26][27][28] to solve the governing equations of the multi-fluid plasma model on a computational grid. [2,[6][7][8] The discontinuous Galerkin method is a finite element approach that allows for arbitrarily high order basis functions to model the variation of the system variables. Source terms are automatically coupled.…”

Section: High-order Discontinuous Galerkin Methodsmentioning

confidence: 99%

“…Recent success with the two-fluid plasma model has provided a development path for plasma simulations that are more physically accurate and capable than MHD models. [1][2][3][4][5][6] Building on the successful development of the two-fluid model, a plasma simulation algorithm is developed for the multi-fluid plasma model. The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid and is, therefore, more physically accurate and capable than MHD models.…”

Section: Executive Summarymentioning

confidence: 99%

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Algorithm Development for the Multi-Fluid Plasma Model

Shumlak¹

2011

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Section: Executive Summarymentioning

confidence: 99%

“…The evolution of the reconnected magnetic flux compares remarkably well with the published data. [2] Additional applications are discussed in more detail below.…”

Section: High-order Discontinuous Galerkin Methodsmentioning

confidence: 99%

Section: High-order Discontinuous Galerkin Methodsmentioning

confidence: 99%

Section: Executive Summarymentioning

confidence: 99%

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Algorithm Development for the Multi-Fluid Plasma Model

Shumlak¹

2011

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“…1(a) and 1(b) with the letters denoting the types of shocks/waves. 6,20,21,36 The part denoted by "SS" is slow shock. As observed, the slow shock structure is greatly altered in the XMHD results.…”

Section: A Brio-wu Shock Tube Testmentioning

confidence: 99%

Computational extended magneto-hydrodynamical study of shock structure generated by flows past an obstacle

Zhao¹,

Seyler

2015

Physics of Plasmas

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The magnetized shock problem is studied in the context where supersonic plasma flows past a solid obstacle. This problem exhibits interesting and important phenomena such as a bow shock, magnetotail formation, reconnection, and plasmoid formation. This study is carried out using a discontinuous Galerkin method to solve an extended magneto-hydrodynamic model (XMHD). The main goals of this paper are to present a reasonably complete picture of the properties of this interaction using the MHD model and then to compare the results to the XMHD model. The inflow parameters, such as the magnetosonic Mach number Mf and the ratio of thermal pressure to magnetic pressure β, can significantly affect the physical structures of the flow-obstacle interaction. The Hall effect can also significantly influence the results in the regime in which the ion inertial length is numerically resolved. Most of the results presented are for the two-dimensional case; however, two three-dimensional simulations are presented to make a connection to the important case in which the solar wind interacts with a solid body and to explore the possibility of performing scaled laboratory experiments.

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Advanced physics calculations using a multi-fluid plasma model

Shumlak

Lilly

Reddell

et al. 2011

Computer Physics Communications

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The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. Derivation of the MHD model involves several asymptotic and simplifying assumptions that can limit its applicability. Therefore, the two-fluid plasma model more accurately represents the appropriate physical processes. Physical parameters indicate the importance of the two-fluid effects: electron to ion mass ratio m e /m i , ion skin depth δ i , and ion Larmor radius r L . The MHD model assumes m e /m i = 0, δ i = 0, and r L = 0. Asymptotic approximations of the two-fluid model, Hall-MHD, has an unbounded Whistler wave that requires artificial dissipation. No unbounded waves exist in the two-fluid model. An algorithm is developed for the simulation of plasma dynamics using the two-fluid and multi-fluid plasma models. The algorithm implements a discontinuous Galerkin method that uses an approximate Riemann solver[1] to compute the fluxes of the fluids and electromagnetic fields at the computational cell interfaces. The two-fluid plasma model has time scales on the order of the electron and ion cyclotron frequencies, the electron and ion plasma frequencies, the electron and ion sound speeds, and the speed of light. Such disparate time scales motivate a semi-implicit time-stepping scheme to overcome the severe time step restrictions of explicit schemes. The algorithm is validated with several test problems including the GEM challenge magnetic reconnection problem [2] and the generation of dispersive plasma waves which are compared to analytical dispersion diagrams. The algorithm is applicable to study advanced physics calculations of plasma dynamics including magnetic plasma confinement and astrophysical plasmas. Three-dimensional solutions of the Z-pinch and the field reversed configuration (FRC) magnetic plasma confinement configurations are presented.

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A discontinuous Galerkin method for the full two-fluid plasma model

Cited by 37 publications

References 16 publications

Algorithm Development for the Multi-Fluid Plasma Model

Algorithm Development for the Multi-Fluid Plasma Model

Computational extended magneto-hydrodynamical study of shock structure generated by flows past an obstacle

Advanced physics calculations using a multi-fluid plasma model

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