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An asymptotic-preserving five-moment two-species plasma model coupled to an external magnetohydrodynamic solver

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read This paper claims that a reformulated Ampère law, discretized with an implicit theta-method, couples a two-species five-moment plasma model to an ideal MHD solver by projecting fast electromagnetic dynamics onto the slow MHD manifold.

desk verdict A useful, honest methods paper on MHD-five-moment coupling, but the 'asymptotic-preserving' label rests on an inherited theorem whose hypotheses are never checked: no test drives ε0→0. read the letter →

arxiv 2607.15019 v1 pith:5EYTRTZZ submitted 2026-07-16 physics.plasm-ph physics.comp-ph

Magnus Deisenhofer , Aleksandr Mustonen , Simon Lautenbach , Rainer Grauer This is my paper · ORCID
classification physics.plasm-phphysics.comp-ph
keywords asymptotic-preservingfive-momenttwo-fluididealMHDcouplingMaxwellequationsquasi-neutrallimitmagneticreconnectionmultiscaleplasmasimulationvariableconversion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to close the last gap in an adaptive hierarchy of plasma models by coupling a two-species, five-moment fluid model (with Maxwell's equations) to an ideal magnetohydrodynamics (MHD) solver. The key claim is that an asymptotic-preserving (AP) implicit discretization, built around a reformulated Ampère law that determines E for any value of the vacuum permittivity ε0, projects fast plasma waves, oscillations, and light waves onto the slow MHD dynamics, so the two models exchange boundary data without spurious reflections or instability. If true, this would let a global simulation use ideal MHD almost everywhere while keeping kinetic-scale physics only in non-ideal regions such as reconnection current sheets. The paper demonstrates the approach with magnetic reconnection tests, including a run that spans the whole hierarchy from kinetic to MHD descriptions.

What carries the argument

The central object is a reformulated Ampère law obtained by equating the two expressions for ∂_t j — one from Maxwell's equations, one from the generalized Ohm's law — giving ε0 ∂_t^2 E + Σ_s (q_s^2/m_s) n_s E + (1/μ0) ∇×∇×E = Σ_s (q_s/m_s)[∇·P_s − j_s×B]. The discretized scheme uses a modified θ-method where the current is approximated as j_s^{n+1} = j_s^{n+1,*} + Δt (q_s^2/m_s) n_s^{n+1} E^{n+1}, leading to a linear system for E^{n+1} and B^{n+1} that is reduced by a Schur complement to inversion of the operator T = (1 + Δt²/ε0 Σ_s q_s² n_s^{n+1}/m_s) + Δt² c² θ² ∇×∇×. The first term acts as a damping factor on E — stronger for large time steps and densities — and is what keeps the scheme

What would settle it

Set up the same reconnection test but in the five-moment/AP region set ε0 = 0 (equivalently c → ∞) and compare the coupled solution against a pure ideal-MHD run; if the two do not converge as ε0 → 0, the scheme is not asymptotic-preserving. A complementary check is to compare the split-step current j^{n+1,*} against a direct evaluation of the generalized Ohm's law in the non-MHD region; inconsistency there would break the AP property at the interface.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that the two-fluid/Maxwell system and ideal MHD can be joined by one numerical scheme with no model-specific switching: a modified θ-method for Maxwell's equations in which the current at the new time level is split into a part computed from the fluid update without E and a linear response Δt C_s E^{n+1}. Combining this with a reformulated Ampère law gives a single implicit equation for E whose operator remains invertible and consistent as ε0→0, so the same solver works in the Maxwell regime and in the quasi-neutral MHD regime. The paper then defines a variable-conversion interface based on center-of-mass quantities and a constant temperature ra

Load-bearing premise

The load-bearing premise is that this specific finite-volume, split-step discretization is asymptotically preserving in the quasi-neutral limit—a property borrowed from a prior particle-scheme proof and never tested by actually letting the vacuum permittivity tend to zero; if the split-step current approximation is not consistent, the seamless transition to ideal MHD is unsupported.

Editorial extensions

If this is right

  • Kinetic-scale physics such as reconnection can be embedded inside a global ideal-MHD simulation without resolving light waves or plasma oscillations in the MHD part.
  • The AP region damps fast waves before they reach the MHD boundary, reducing spurious reflections that appear in reference runs with conducting boundaries.
  • The full model hierarchy—from fully kinetic Vlasov down to five-moment and ideal MHD—can be run in a single coupled simulation, as demonstrated for magnetic reconnection.
  • Coupling an external MHD solver requires only overwriting boundary blocks with converted two-fluid data and filling ghost cells from MHD data, so existing MHD codes need minimal modification.
  • The variable conversion using center-of-mass definitions and a constant temperature ratio preserves mass, momentum, and particle energy, while intentionally not conserving total electromagnetic energy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the AP property is confirmed for this discretization, the same reformulated-Ampère-law template could apply to other fluid moment hierarchies, because the current-response term depends only on the species charge-to-mass ratio and density.
  • The constant temperature-ratio assumption α_T is the most physically fragile input; in realistic magnetospheres where Te/Ti varies, the interface conversion will introduce errors that the paper's Harris-sheet tests do not exercise.
  • A direct numerical check driving ε0 toward zero in the five-moment region while comparing against a pure ideal-MHD solution would settle whether the claimed asymptotic consistency holds for the finite-volume split-step implementation.
  • The demonstrated damping of fast oscillations at AP regions suggests the scheme could double as a wave-absorbing buffer, but it also implies physical high-frequency fluctuations crossing the interface are intentionally suppressed, which may matter for turbulence studies.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes an asymptotic-preserving (AP) discretization of the two-species five-moment plasma model coupled to Maxwell's equations, and couples it to an external ideal MHD solver through a variable-conversion interface. The AP scheme follows Degond et al. (2017): a modified θ-method is used for the electromagnetic fields, with the current implicitly advanced using a split-step predictor, leading to a Schur-complement system for the electric field. The coupling interface converts between two-fluid and MHD variables using center-of-mass definitions and a constant temperature ratio α_T. The method is implemented in the muphyII framework and tested on GEM magnetic reconnection setups, including a simulation spanning the entire fluid hierarchy from ten-moment to MHD. The paper claims that this provides a seamless, asymptotically consistent bridge between kinetic-scale models and ideal MHD.

Significance. If the AP property is indeed realized by the proposed discretization, this work is a significant contribution to multiscale plasma modeling: it completes the muphyII hierarchy down to ideal MHD and enables global simulations with embedded non-ideal regions. The derivation of the reformulated Ampère law (2.34), the implicit system (2.41–2.42), and the Schur-complement solve (2.51–2.54) are coherent and useful. The coupling architecture via MPI intercommunicators is modular and practical. The validation against finer reference models in the same code is appropriate verification at finite speed of light. However, the defining claim of asymptotic preservation is not verified for the specific spatial discretization, and no numerical test actually drives ε0→0. The paper therefore currently supports stable coupling at finite ε0, but not the central 'seamless projection' claim.

major comments (3)
  1. [Sec. 2.2, Eqs. (2.41)–(2.42), (2.54)] The paper states that the modified θ-method leads to a consistent discretization of (2.34) 'given a suitable spatial discretisation', citing Degond et al. (2017). However, it does not verify that the finite-volume/staggered-grid spatial discretization used here satisfies the required compatibility conditions. In particular, no discrete div B preservation property is established for the Faraday–Ampère pair, and no analysis is given for the null space of the discrete curl-curl operator in (2.54). This is load-bearing because the AP property is the central claim; without such verification, the consistency of the AP update in the ε0→0 limit is merely inherited from the reference paper, not established for the present scheme.
  2. [Sec. 5, Figs. 4–6, 8–10] All numerical tests use a reduced speed of light c=20 v_A, i.e., a finite ε0. The agreement with F5eF5iM and F10eF10iM reference runs demonstrates that the coupled scheme is stable and accurate at this finite ε0, but it does not test the defining ε0→0 limit. To support the abstract's claim of 'seamlessly projects these fast dynamics onto the slow MHD dynamics', a convergence study with increasing c (or decreasing ε0) and comparison against an MHD-only reference is required. Without such a test, the asymptotic-preserving property is not demonstrated by the numerical evidence.
  3. [Sec. 2.2, Eqs. (2.43)–(2.50)] The consistency of the AP scheme depends on the predictor j^{n+1,*} for the current. The paper proposes a first-order split-step update for the fluid variables with E=0, followed by an Euler step for the E-source. It is not shown that this predictor is a consistent approximation in the sense required by Degond et al. (2017), nor is its order of accuracy stated. Since the AP property relies on this consistency, a missing analysis or at least a numerical verification of the predictor's convergence is a gap in the derivation.
minor comments (5)
  1. [Sec. 2, before Eq. (2.8)] Typo: 'evolution if the electric field' should read 'evolution of the electric field'.
  2. [Sec. 2.1, Eq. (2.14)] The derivation of the generalized Ohm's law (2.14) from (2.13) is not shown in detail; the factors of m_e/m_i appear non-obvious. A short intermediate step would help the reader verify the equation.
  3. [Sec. 3, Eqs. (3.6)–(3.10)] The constant temperature ratio α_T is introduced as an assumption and the paper acknowledges it may not hold in realistic settings. Since the interface conversion relies on this parameter, it would be useful to quantify its effect, e.g., by running a sensitivity test or at least stating the expected error magnitude.
  4. [Fig. 3] The time-stepping diagram is dense and the caption could be expanded to explain the meaning of the colored arrows and the staggered FDTD offsets more clearly.
  5. [Sec. 4.2] The test program is described as using CWENO reconstruction, but the cited reference (Kurganov & Levy 2000) is a central scheme with limiter. Please clarify the exact reconstruction method.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the AP update is a parameter-free discretization, the MHD reduction is textbook, and the α_T closure is declared rather than fitted.

full rationale

The central derivation chain is not circular. The AP discretization (2.41)-(2.42) is constructed from the reformulated Ampère law (2.34), which follows by equating two independent expressions for ∂_t j: one from Maxwell's equations (2.32) and one from the two-fluid generalized Ohm's law (2.33). No term in the final operator T (2.54) is fitted, and the scheme is not defined in terms of the reconnection quantities it later predicts. The mass-limit reduction in Sec. 2.1 to ideal Ohm's law and the MHD conservation form (2.30) is a standard asymptotic derivation with explicit assumptions (m_e→0, ε0→0, quasi-neutrality, small Hall and electron-pressure terms); it does not import the target result. The AP consistency is attributed to Degond et al. (2017), an external source with stated conditions; the paper's failure to verify those conditions for its finite-volume/split-step discretization and its use of finite c=20 v_A in all tests are validation gaps, not circular reductions. The temperature-ratio α_T is presented as a modeling assumption, explicitly acknowledged in Sec. 3 as not necessarily constant in realistic domains, and is not calibrated to the reconnection output. The coupled runs are compared to finer reference models in the same code, which is legitimate code verification rather than fitting. Self-citations to muphyII and closures are contextual and not load-bearing for the AP claim; no uniqueness theorem from the authors is invoked to exclude alternatives. Accordingly, no step reduces by construction or self-citation to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The ledger shows the method pulls most of its physics from prior literature (two-fluid equations, MHD limiting, Degond et al.'s AP framework) rather than postulating new entities — no invented physical quantities. The genuinely new contributions (FV-AP discretization, Schur-complement solve, coupling protocol) rest on the unverified transfer of Degond's AP-consistency conditions, the asserted consistency of the split-step predictor, and a user-supplied temperature ratio α_T for the energy split at the interface. The ε0→0 limit that defines the AP property is never exercised in the numerical tests.

free parameters (4)
  • Temperature ratio α_T = T_e/T_i for MHD→two-fluid energy split = initial GEM ratio, fixed per run (Sec. 5)
    The MHD→two-fluid conversion must split one total thermal energy into electron and ion energies (Eqs. 3.8–3.10); α_T is a user-supplied modeling choice, set to the initial GEM ratio in the tests. The paper notes it 'is not necessarily constant throughout the domain' in realistic settings. Not fitted to simulation output.
  • Reduced speed of light in non-MHD regions = c = 20 v_A,0
    Non-MHD regions use a reduced speed of light, a standard computational choice; it keeps ε0 finite, so the ε0→0 limit the AP scheme is designed for is never exercised in the tests.
  • Ion-to-electron mass ratio in tests = 25 (Sec. 5.1), 1836 (Sec. 5.2)
    Test design choice: m_i/m_e = 25 in Sec. 5.1 deliberately violates the m_e→0 asymptotic limit to stress the coupling; m_i/m_e = 1836 in Sec. 5.2. Not a method parameter, but it sets the scale separation the coupling must bridge.
  • θ-method parameter of AP time discretization = θ = 1
    θ = 1 in all tests. At θ = 0 the scheme reduces to the damped explicit update (Eq. 2.55); the paper does not test intermediate θ values.
assumptions (5)
  • domain assumption Degond et al. (2017): the modified θ-method (Eqs. 2.41–2.42) is a consistent discretisation of the reformulated Ampère law (2.34) for both ε0≠0 and ε0=0, given a 'suitable spatial discretisation' and a consistent j^{n+1,*} approximation.
    Invoked in Sec. 2.2 as the basis of the AP property; the FV spatial discretization and split-step predictor of this paper are not shown to satisfy the stated conditions, and no ε0→0 test is provided.
  • domain assumption First-order operator splitting (Eqs. 2.43–2.50) yields a consistent predictor j^{n+1,*} for the implicit E-update (Eq. 2.39).
    The consistency of the split-step approximation is asserted, not demonstrated; it enters the AP right-hand side and thus the whole implicit solve.
  • domain assumption Ideal MHD is valid in the outer regions: |j×B|/en ≪ |u×B| and |∇p_e|/en ≪ |E| (Eqs. 2.19–2.20).
    These ordering assumptions justify replacing Hall/electron-pressure terms by ideal Ohm's law and determine where the MHD model is used in the domain decomposition (Sec. 5).
  • domain assumption Quasi-neutrality n_e = n_i in the MHD→two-fluid conversion (Eq. 3.2).
    Inherited from the ε0→0 limit; used to invert the variable conversion (3.2)–(3.4), including the electron/ion velocity split that requires j_MHD from Ampère's law.
  • domain assumption The five-moment isotropic-pressure closure (Eqs. 2.1–2.3) represents non-ideal regions, and the existing muphyII hierarchy couplings (Vlasov, 10-moment, hybrid) work as described in Allmann-Rahn et al. (2024) and Lautenbach & Grauer (2018).
    Self-cited prior work that the paper builds on without independent verification; the abstract's 'from kinetics to ideal MHD' claim depends on it, while the demonstrated hierarchy is limited to fluid models (Sec. 5.2).

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Cite this review

Pith. "Pith review of An asymptotic-preserving five-moment two-species plasma model coupled to an external magnetohydrodynamic solver." pith.science (2026). https://pith.science/paper/5EYTRTZZ

@misc{pith2026260715019,
  author       = {Pith},
  title        = {Pith review of: An asymptotic-preserving five-moment two-species plasma model coupled to an external magnetohydrodynamic solver},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5EYTRTZZ}},
  note         = {Machine review of arXiv:2607.15019}
}
read the original abstract

Accurately modeling collisionless space plasmas requires capturing small-scale kinetic effects while keeping global-scale simulations computationally tractable. Traditional multiscale approaches often rely on localized magnetohydrodynamics (MHD)-particle-in-cell (PIC) coupling or dynamic model hierarchies. In this work, we extend an established, adaptive multi-model hierarchy spanning from fully kinetic Vlasov descriptions to fluid models by introducing an asymptotic-preserving (AP) strategy that couples a two-species, five-moment fluid description with an ideal MHD solver. This coupling is the final critical step toward enabling efficient global simulations because the kinetic-scale physics in nonideal regions is entirely handled by finer models in the hierarchy. Kinetic descriptions natively solve Maxwell's equations and thus capture fast plasma waves, oscillations, and light waves, which are absent in the MHD dynamics. To address this difference without sacrificing computational efficiency, our AP framework seamlessly projects these fast dynamics onto the slow MHD dynamics, ensuring rigorous consistency at the model interfaces. We detail the AP two-fluid formulation, the variable-coupling interface, and its integration into external frameworks. Finally, we demonstrate the validity and robustness of the fully coupled framework, from kinetics to ideal MHD, through magnetic reconnection simulations.

Figures

Figures reproduced from arXiv: 2607.15019 by the authors.

Figure 1
Figure 1. Current state of the scheme hierarchy implemented in muphyII in relation to ideal MHD, showing the models used for each plasma description and the required coupling. Rieke et al. (2015); Lautenbach & Grauer (2018); Allmann-Rahn et al. (2024), involves coupling a hierarchy of models with varying complexity based on criteria that dynamically determine the appropriate modeling. Building on this, we propose extending th… view at source ↗
Figure 2
Figure 2. Sketch of our envisioned muphyII-AMR coupling. Both simulations span the whole domain, however only a part of the highest refinement level is being simulated by muphyII while the rest of the domain is exclusively simulated and stored by the external MHD code. A coupling layer (coloured red) at the edge of the muphyII region bridges the different electromagnetic models and time stepping approaches. 4. Coupling to ext… view at source ↗
Figure 3
Figure 3. Logical steps in one time step of the AP scheme and neighbouring schemes, along with boundary data exchanges between them. The order of operations is from top to bottom. F denotes the set of fluid variables. Red arrows indicate boundary data exchange. Algorithm 2: Coupled External MHD Solver Step External::step: (ρ n+1 ,(ρu) n+1 , E n+1 , B n+1) ← Integrator(ρ n ,(ρu) n , E n , B n , ∆t) ∆t ← Maxdt(ρ n+1 ,(ρu) n+1 ,… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Bx of the coupled and reference simulations of magnetic reconnection. −4π −2π 0 2π F5eF5iM Ez t = 0.0tend t = 0.7tend t = 1.0tend 0 2π 4π 6π −4π −2π 0 2π Coupled Ez MHD AP F5eF5iM AP MHD 0 2π 4π 6π 0 2π 4π 6π −0.50 −0.25 0.00 0.25 0.50 −0.4 −0.2 0.0 0.2 0.4 [PITH_FULL…
Figure 5
Figure 5. Figure 5: Ez of the coupled and reference simulations of magnetic reconnection. fast oscillations developing as the reconnection starts. As the Harris sheet setup uses conducting boundary conditions, these waves are reflected at the boundaries of the domain for the reference sim…
Figure 6
Figure 6. Figure 6: jx of the coupled and reference simulations of magnetic reconnection. −16π −12π −8π −4π 0 4π 8π 12π −8π −4π 0 4π MHD AP F5eF5iM F5eF10iM F10eF10iM [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Decomposition of the simulated domain into regions using different schemes. 5.2. Testing the full model hierarchy from the 10 moment-two fluid to the MHD model In addition to the change in mass ratio, we double the domain size compared to Sec. 5.1 to Lx = 32πdi,0 and L…
Figure 8
Figure 8. Figure 8: jz of the coupled and reference simulations of magnetic reconnection. −8π −4π 0 4π F10eF10iM By t = 0.0tend t = 0.7tend t = 0.9tend 0 4π 8π 12π −8π −4π 0 4π Coupled By 0 4π 8π 12π 0 4π 8π 12π −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: By of the coupled and reference simulations of magnetic reconnection. as well as a reference simulation using F10eF10iM, simulated again to tend = 40Ω −1 i . The results of the two simulations match closely and none of the transitions between different schemes develop …
Figure 10
Figure 10. Figure 10: Ez of the coupled and reference simulations of magnetic reconnection. 6. Conclusions and Outlook In this work, we have presented a comprehensive multiscale framework for simulat￾ing collisionless space plasmas that bridges kinetic-scale physics with large-scale MHD dy…

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Works this paper leans on

29 extracted references · 1 canonical work pages

  1. [1]

    , Lautenbach, S

    Allmann-Rahn, F. , Lautenbach, S. , Deisenhofer, M. & Grauer, R. 2024 The muphyII code: Multiphysics plasma simulation on large HPC systems . Computer Physics Communications 296 , 109064

    2024

  2. [2]

    , Lautenbach, S

    Allmann-Rahn, F. , Lautenbach, S. , Grauer, R. & Sydora, R. D. 2021 Fluid simulations of three-dimensional reconnection that capture the lower-hybrid drift instability . Journal of Plasma Physics 87 , 905870115

    2021

  3. [3]

    , Trost, T

    Allmann-Rahn, F. , Trost, T. & Grauer, R. 2018 Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection . J. Plasma Phys. 84 , 905840307

    2018

  4. [4]

    , Bangerth, W

    Arndt, D. , Bangerth, W. , Bergbauer, M. , Blais, B. , Fehling, M. , Gassm\" o ller, R. , Heister, T. , Heltai, L. , Kronbichler, M. , Maier, M. , Munch, P. , Scheuerman, S. , Turcksin, B. , Uzunbajakau, S. , Wells, D. & Wichrowski, M. 2025 The deal.ii library, version 9.7 . Journal of Numerical Mathematics 33 (4), 403--415

    2025

  5. [5]

    , Drake, J

    Birn, J. , Drake, J. F. , Shay, M. A. , Rogers, B. N. , Denton, R. E. , Hesse, M. , Kuznetsova, M. , Ma, Z. W. , Bhattacharjee, A. , Otto, A. & Pritchett, P. L. 2001 Geospace environmental modeling (gem) magnetic reconnection challenge . Journal of Geophysical Research: Space Physics 106 (A3), 3715--3719 , arXiv:arXiv: https://agupubs.onlinelibrary.wiley....

    doi:10.1029/1999ja900449 2001

  6. [6]

    Burby, J. W. 2017 Magnetohydrodynamic motion of a two-fluid plasma . Physics of Plasmas 24 (8), 082104

    2017

  7. [7]

    , Deluzet, F

    Crestetto, A. , Deluzet, F. & Doyen, D. 2020 Bridging kinetic plasma descriptions and single-fluid models . Journal of Plasma Physics 86 , 825860501

    2020

  8. [8]

    & Fang , Y.-L

    Dalcin , L. & Fang , Y.-L. L. 2021 mpi4py: Status Update After 12 Years of Development . Computing in Science and Engineering 23 (4), 47--54

    2021

Show all 29 references
  1. [9]

    Daldorff, L. K. , Tóth, G. , Gombosi, T. I. , Lapenta, G. , Amaya, J. , Markidis, S. & Brackbill, J. U. 2014 Two-way coupling of a global hall magnetohydrodynamics model with a local implicit particle-in-cell model . Journal of Computational Physics 268 , 236--254

    2014

  2. [10]

    , Deluzet, F

    Degond, P. , Deluzet, F. & Doyen, D. 2017 Asymptotic-preserving particle-in-cell methods for the V lasov– M axwell system in the quasi-neutral limit . Journal of Computational Physics 330 , 467--492

    2017

  3. [11]

    , Dolence, J

    Grete, P. , Dolence, J. C. , Miller, J. M. , Brown, J. , Ryan, B. , Gaspar, A. , Glines, F. , Swaminarayan, S. , Lippuner, J. , Solomon, C. J. , Shipman, G. , Junghans, C. , Holladay, D. , Stone, J. M. & Roberts, L. F. 2023 Parthenon—a performance portable block-structured ada...

    2023

  4. [12]

    , Datta, I

    Ho, A. , Datta, I. A. M. & Shumlak, U. 2018 Physics-based-adaptive plasma model for high-fidelity numerical simulations . Frontiers in Physics 6 , 105

    2018

  5. [13]

    , Tenerani, A

    Hunana, P. , Tenerani, A. , Zank, G. P. , Goldstein, M. L. , Webb, G. M. , Khomenko, E. , Collados, M. , Cally, P. S. , Adhikari, L. & Velli, M. 2019 An introductory guide to fluid models with anisotropic temperatures. part 2. kinetic theory, padé approximants and landau fluid...

    2019

  6. [14]

    1999 Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations

    Jin, S. 1999 Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations . SIAM Journal on Scientific Computing 21 (2), 441--454 , arXiv:arXiv: https://doi.org/10.1137/S1064827598334599

    1999 doi

  7. [15]

    & Levy, D

    Kurganov, A. & Levy, D. 2000 A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations . SIAM Journal on Scientific Computing 22 (4), 1461--1488 , arXiv:arXiv: https://doi.org/10.1137/S1064827599360236

    2000 doi

  8. [16]

    & Grauer, R

    Lautenbach, S. & Grauer, R. 2018 Multiphysics simulations of collisionless plasmas . Frontiers in Physics 6 , 113

    2018

  9. [17]

    , Lübke, J

    Lautenbach, S. , Lübke, J. , Innocenti, M. E. , Kormann, K. & Grauer, R. 2026 Optimal landau-type closure parameters for two-fluid simulations of plasma turbulence at kinetic scales . Journal of Plasma Physics 92 (1), E8

    2026

  10. [18]

    , Olshevsky, V

    Markidis, S. , Olshevsky, V. , Tóth, G. , Chen, Y. , Peng, I. B. , Lapenta, G. & Gombosi, T. 2021 Kinetic Modeling in the Magnetosphere\/ , chap. 38, pp. 607--615 . American Geophysical Union (AGU)

    2021

  11. [19]

    Message Passing Interface Forum 2023 MPI : A Message-Passing Interface Standard Version 4.1\/

    2023

  12. [20]

    & Burby, J

    Miloshevich, G. & Burby, J. W. 2021 Hamiltonian reduction of V lasov- M axwell to a dark slow manifold . Journal of Plasma Physics 87 (3), 835870301

    2021

  13. [21]

    , Hakim, A

    Ng, J. , Hakim, A. , Wang, L. & Bhattacharjee, A. 2020 An improved ten-moment closure for reconnection and instabilities . Physics of Plasmas 27 (8), 082106

    2020

  14. [22]

    , Trost, T

    Rieke, M. , Trost, T. & Grauer, R. 2015 Coupled Vlasov and two-fluid codes on GPU s . Journal of Computational Physics 283 , 436 -- 452

    2015

  15. [23]

    , Gassner, G

    Schlottke-Lakemper, M. , Gassner, G. J. , Ranocha, H. , Winters, A. R. , Chan, J. & Rueda-Ramírez, A. 2025 T rixi.jl: A daptive high-order numerical simulations of hyperbolic PDE s in J ulia. https://github.com/trixi-framework/Trixi.jl

    2025

  16. [24]

    , Tenishev, V

    Shou, Y. , Tenishev, V. , Chen, Y. , Toth, G. & Ganushkina, N. 2021 Magnetohydrodynamic with adaptively embedded particle-in-cell model: Mhd-aepic . Journal of Computational Physics 446 , 110656

    2021

  17. [25]

    & Osher, S

    Shu, C.-W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes . Journal of Computational Physics 77 (2), 439--471

    1988

  18. [26]

    Sulem, P. L. & Passot, T. 2015 Landau fluid closures with nonlinear large-scale finite larmor radius corrections for collisionless plasmas . Journal of Plasma Physics 81 (1), 325810103

    2015

  19. [27]

    The Open MPI Development Team 2025 Open MPI : Open source high performance computing

    2025

  20. [28]

    , Hakim, A

    Wang, L. , Hakim, A. H. , Bhattacharjee, A. & Germaschewski, K. 2015 Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection . Physics of Plasmas 22 (1), 012108

    2015

  21. [29]

    , Chen, Y

    Wang, X. , Chen, Y. & Tóth, G. 2022 Global magnetohydrodynamic magnetosphere simulation with an adaptively embedded particle-in-cell model . Journal of Geophysical Research: Space Physics 127 (8), e2021JA030091

    2022

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.