A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

Loverich, John; Hakim, Ammar; Shumlak, U.

doi:10.4208/cicp.250509.210610a

Cited by 55 publications

(51 citation statements)

References 49 publications

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“…The discontinuous Galerkin method is selected for its robustness to work well for kinetic equations in phase space, Maxwell's electromagnetic equations, and fluid equations in physical space with multiple contemporary examples for these application areas [12,13,14,15,16,17,18]. Additionally, the explicit method is straightforward to implement and well suited for emerging high performance computing architectures as described in Chapters 4 and 9.…”

Section: Methodsmentioning

confidence: 99%

“…With fluctuations in physical space propagating only as perturbation of these macroscopic parameters, a fluid model is appropriate [2,10,11,12]. The Euler-fluid plasma model equations adequately describe compressible inviscid fluid,…”

Section: Euler -Maxwell Fluid Modelmentioning

confidence: 99%

“…[6] describes a two-species plasma initial configuration targeted for the study of reconnection. The problem has been studied many times with models ranging from ideal MHD, multi-fluid plasma [12], extended moment models [51,52,53,54], and kinetic models. Kinetic models include Particle-in-Cell [55,56], Vlasov-Darwin [57], and VlasovMaxwell [58].…”

Section: Gem Magnetic Reconnection Challenge Problemmentioning

confidence: 99%

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A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Reddell¹

2016

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A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case.The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves.A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures.WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation.The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.

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Section: Methodsmentioning

confidence: 99%

Section: Euler -Maxwell Fluid Modelmentioning

confidence: 99%

Section: Gem Magnetic Reconnection Challenge Problemmentioning

confidence: 99%

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A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Reddell¹

2016

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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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“…Simulations were performed using the USim code (formerly called Nautilus) [42,43]. Algorithms on which USim is based have been verified against shock-relevant problems [44,45]. In the simulations, the jets are assumed to be 100% Ar ii with initial n e = n i = 10 14 cm −3 , T e = T i = 1.4 eV, and velocities of ±6.2 km/s (i.e., transverse component of V jet ≈ 30 km/s).…”

mentioning

confidence: 99%

Experimental Characterization of the Stagnation Layer between Two Obliquely Merging Supersonic Plasma Jets

Merritt

Hsu

et al. 2013

Phys. Rev. Lett.

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We present spatially resolved measurements characterizing the stagnation layer between two obliquely merging supersonic plasma jets. Intra-jet collisionality is very high (λii ≪ 1 mm), but the inter-jet ion-ion mean free paths are on the same order as the stagnation layer thickness (a few cm). Fast-framing camera images show a double-peaked emission profile transverse to the stagnation layer, with the central emission dip consistent with a density dip observed in the interferometer data. We demonstrate that our observations are consistent with collisional oblique shocks.Colliding plasmas have been studied in a variety of contexts, e.g., counterstreaming laser-produced plasmas supporting hohlraum design for indirect-drive inertial confinement fusion [1][2][3], forming and studying astrophysically relevant shocks [4][5][6][7][8], and for applications such as pulsed laser deposition [9] and laser-induced breakdown spectroscopy [10]. Physics issues arising in these studies include plasma interpenetration [11][12][13][14][15][16], shock formation [17], and the formation and dynamics of a stagnation layer [18][19][20]. In this work, we present experimental results on two obliquely merging supersonic plasma jets, which are in a different and more collisional parameter regime than many of the colliding plasma examples mentioned above. Ours and other recent jet-merging experiments [21,22] were conducted to explore the feasibility of forming imploding spherical plasma liners via an array of merging plasma jets [23][24][25][26][27], which could have applications in forming cm-, µs-, and Mbar-scale plasmas for fundamental high-energy-density-physics studies [28] and as a standoff driver for magnetoinertial fusion [23,[29][30][31][32]. Prior experiments studying the stagnation layer between colliding laser-produced or wire-array z-pinch [33] plasmas were on smaller spatial scales (mm or smaller) that could not be fully resolved by measurements. New results in the present work are the experimental identification and characterization of a few-cm thick stagnation layer between colliding plasmas, and the demonstration that our observations are consistent with hydrodynamic oblique shock theory [34].Experiments reported here are conducted on the Plasma Liner Experiment (PLX) [35], in which two supersonic argon plasma jets are formed and launched by plasma railguns [36]. Plasma jet parameters at the exit of the railgun nozzle (peak n e ≈ 2 × 10 16 cm −3 , peak T e ≈ 1.4 eV, V jet ≈ 30 km/s, Mach number M ≡ V jet /C s,jet ≈ 14, diameter = 5 cm, and length ≈ 20 cm) and their evolution during subsequent jet propagation have been characterized in detail [35]. The jet magnetic field inside the railgun is ∼3 T, but the classical magnetic diffusion time is a few µs [35], and thus • apart, two merging plasma jets, R-Z coordinates used in the paper, approximate interferometer/spectrometer linesof-sight (Z ≈ 84 cm), and CCD camera field-of-view.we ignore the effects of a magnetic field by the time of jet merging (> 20 µs). Experimental data ...

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A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

Cited by 55 publications

References 49 publications

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

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

Experimental Characterization of the Stagnation Layer between Two Obliquely Merging Supersonic Plasma Jets

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