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Astrophysical Weighted Particle Magnetohydrodynamics

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Evghenii Gaburov, Keigo Nitadori

Instrumentation and Methods for Astrophysics · Submitted 21 Jun 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks.

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arXiv ID1006.4159 (version 1)
Pith IDWRIXWRF3, Pith's permanent record of this paper and its review
CitationEvghenii Gaburov, Keigo Nitadori. "Astrophysical Weighted Particle Magnetohydrodynamics." arXiv:1006.4159 (2010). https://pith.science/paper/WRIXWRF3
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,153 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.87 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.28 · mentions code or data availability 0.05.

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arXiv listing abstract v1. Results and the main claim are underlined; .

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. contribution 1.00 0.88 0.11 asserted 1.00
s1 The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. method 0.78 0.89 0.08 asserted 1.00
s2 The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. method 1.00 0.63 0.03 asserted 1.00
s3 As a result, necessary diffusion which is required to treat dissipative processes is added automatically. method 0.38 0.76 0.06 asserted 1.00
s4 As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. result 0.55 0.88 0.18 asserted 1.00
s5 The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. method 0.54 0.47 0.10 asserted 0.87
s6 The scheme is validated in several hydrodynamic and MHD test cases. method 0.55 0.93 0.07 asserted 1.00
s7 In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks. contribution 0.56 0.94 0.45 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks.

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References
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5 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Uses its method or tool 2 papers
  • Following [ref] , the source term $(VS)_i$ in Eq. [ref] for particle $i$ is [equation] [equation] [equation] where $𝐁̅_x,ij^'$ and $ψ̅_ij$ are the combination of the normal component of the magnetic field $𝐁_x^'$ with respect to area elements and $ψ$, their forms read [equation] [equation] We set $𝐯_x^'$ as projected speed with respect to the frame, then $c_h = 𝐯_x^' + c_+$, $𝐯_x^' + c_±$ is the fast/slow magnetosonic wave speed, [equation] Here, $a=√(γP/ρ)$ is the sound speed, $c̃_h,ij = max{c_+,i,c_+,j}$, and $τ_i = L_i/(c_rc_h,i)$, $L_i$ is an effective size of the particle ($L_i = V_i,√(2V_i/π),(3V_i/4π)^1/3$ for 1D, 2D, and 3D, respectively) and the constant $c_r$ is equal to 0.03 [ref] .

    Meshless Methods for Magnetohydrodynamics with Vector Potential · Meshless discretization · 0.99

  • An alternative approach to modelling fluid flow with particles is offered by weighted meshless schemes [ref] , as implemented in the MFV and MFM methods used in GIZMO [ref] .

    Computational approaches to modeling dynamos in galaxies · Particle methods · 0.90

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