An energy-consistent numerical scheme for plasma simulations reproduced the linear growth of the parametric-decay and firehose instabilities, but its fourth- and sixth-order versions failed within a few time steps in one extremely low-beta blast-wave test. The second-order version remained stable in that reported case, which was part of a seven-problem numerical benchmark suite.
A scheme built around energy accounting
The work centers on an energy-consistent finite-difference scheme for 10-moment magnetohydrodynamics, or MHD, a model that uses a pressure tensor to represent pressure differences by direction and off-diagonal pressure stresses. The scheme filters all six independent pressure-tensor components. It then transfers the kinetic and magnetic energy dissipated by that filtering into the diagonal pressure components, dividing it equally among them under an equipartition assumption. The method is designed for a broad range of plasma beta.
The proposed scheme was validated against seven numerical test problems under isotropic, gyrotropic and no-isotropization/gyrotropization conditions. The suite covered circularly polarized Alfven-wave propagation, parametric decay, a shock tube, the Orszag-Tang vortex, firehose instability, a blast wave and magnetic reconnection. All of the test simulations used third-order SSP-RK3 time integration.
Where the numerical tests held up
In the circularly polarized Alfven-wave test, the second-order MUSCL scheme showed L1 convergence as the grid was refined. The fourth- and sixth-order schemes instead saturated as resolution increased, meaning their reported error plateaued at fine resolution.
As the time-step setting called CFL was varied, the total-energy conservation error scaled as CFL^3, consistent with the SSP-RK3 integrator used throughout the tests.
The scheme reproduced the linear growth of the parametric-decay and firehose instabilities. In the shock-tube test, the second-order result was nearly monotonic, while higher-order results oscillated around discontinuities. Nonlinear filtering suppressed those oscillations. In the Orszag-Tang vortex test, fourth- and sixth-order schemes resolved smaller-scale structures than the second-order scheme. The divergence error could be removed without crashing, and anisotropic effects were captured qualitatively.
A boundary in the hardest test
In the blast-wave benchmark, a system with beta about 10^-10, fourth- and sixth-order schemes failed within a few time steps, while the second-order scheme remained stable. This was one reported test within the seven-problem numerical suite.
The result is a boundary on the reported evidence, not a general verdict on all higher-order runs. It establishes second-order stability in that blast-wave case, while higher-order stability was not established there.
Reconnection results in separate configurations
The isotropic reconnection run developed bidirectional outflows. Reconnected flux increased to nearly 5, with a reconnection rate of about 0.05.
In the gyrotropic run, reconnected flux increased to nearly 4 and the reconnection rate was about 0.02 to 0.03. The no-relaxation case developed no appreciable reconnection outflow.
The paper's stated limits
The authors identify the reported higher-order crashes in extremely low beta as a limitation. The model also assumes zero heat flux, equipartitioned numerical heating has not been quantitatively tested against alternative partitions, and Hall and explicit gyration effects remain unimplemented.
Preprint status and access
The document is an arXiv preprint, version 1, dated 26 Aug 2026. The simulation code is openly available in a GitHub repository at https://github.com/keita-akutagawa, while simulation results are available from the corresponding author upon reasonable request.
Support came from JSPS KAKENHI Grants JP24K00688, JP25K00976 and JP25K01052, the NINS Joint Research program OML032402, and the JST Sogyo Program Stage 2 grant JPMJSF2503. The authors declare no known competing financial interests or personal relationships that could have appeared to influence the work.
Paper data and sources
Original title: A generalized energy-consistent finite difference scheme for 10-moment magnetohydrodynamics
Authors: Keita Akutagawa, Shinsuke Imada, Munehito Shoda
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text