Dartmouth Events

Abstract: The traditional Lagrangian and Eulerian fluid representations do not trivially lead to numerically stable schemes. It can be shown that this is caused by an inconsistency between continuous and discrete conservation laws, since discrete operators need not satisfy the Leibniz product rule. We demonstrate a new fluid representation that bypasses this fundamental problem by constructing an anti-symmetric flow operator that acts on generalized moment-like quantities related to quadratic invariants of the system [1]. Numerical implementations automatically inherit the most important conservation properties of the continuous system through simple analogy. The plasma flow is interpreted as a time-reversible infinitesimal rotation, which guarantees a discrete inverse. Mass and energy positivity are trivially preserved. Finally, it can be shown that the discrete models resulting from this approach are symplectic and unconditionally stable. The method is completely general, as it only involves expressing the model in a different reference frame. Hence, it is widely applicable and essentially independent of the desired numerical method. It does allow, however, that stiff and strongly non-linear problems be integrated using centered finite differences. We have applied our methodology to the Braginskii two-fluid model, the magnetohydrodynamics (MHD) equations, and also more computationally efficient drift-ordered models. The conservation properties are verified using representative cases such as single seeded blob dynamics and the Orzsag-Tang vortex, obtaining high-fidelity simulation results with negligible dissipation.