Numerical-heating partition among pressure components

Determine an appropriate partition of numerical heating among the diagonal and off-diagonal components of the pressure tensor in the energy-consistent finite-difference scheme, and assess how alternative partitioning strategies affect pressure-tensor evolution.

Background

The scheme transfers numerical heating generated by filtering into the pressure tensor and adopts equipartition among the three diagonal components, with off-diagonal heating set to zero in the fiducial setup. The paper notes that this assumption has not been quantitatively compared with alternative strategies, leaving the physically and numerically appropriate heating partition unresolved.

References

The third is that we assumed the equipartition of the numerical heating among the three diagonal pressure components without quantitatively verifying this assumption against alternative partitioning strategies. Determining how to partition the numerical heating, and assessing its impact on the pressure tensor evolution, is also one of the remaining tasks.

— A generalized energy-consistent finite difference scheme for 10-moment magnetohydrodynamics  (2608.25441 - Akutagawa et al., 26 Aug 2026) in Section 6, Conclusion