Improved Darwin PIC algorithm

The application of the Darwin field algorithm to PIC simulation presents two challenges: 1) Coulomb gauge must be achieved to high accuracy; 2) time centering is not natural (as in the case of EM PIC). Using the previously-reported [1] solenoidal FE representation, Coulomb gauge is point-wise satisfied. Extending this previous work, the general scheme of Lapenta [2] and Markedis for “Energy-conserving PIC” is adapted to the time-stepping issue. The resulting algorithm is time-centered, almost energy-conserving, and absolutely stable. In contrast to the method of Ref. 2, the issue of charge conservation is moot, i.e. charge is exactly conserved by the Darwin separation of ES and MS components. 2D tests with time steps beyond explicit stability limits repeating the successful tests of Ref. 1.are reported. Extensions to arbitrary-magnetization, multi-species, 3D, and to hybrid models with some or all fluid species are discussed.



[1] D. C. Barnes, J. Comp. Phys. 462, 11151 (2022).

[2] Giovanni Lapenta, J. Comp. Phys. 334, 349 (2017).