April 15-17

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Author: Federico D Halpern
Requested Type: Poster
Submitted: 2019-02-21 17:20:47

Co-authors: R.E. Waltz, M. Kostuk

Contact Info:
General Atomics
P.O. Box 85608
San Diego, California   92186-5
United States

Abstract Text:
The traditional Lagrangian and Eulerian representation of the fluid equations do not trivially lead to numerically stable schemes. It can be easily 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]. There are important advantages and features in the new representation. Numerical implementations inherit important conservation properties of the continuous system through analogy. Plasmas flows are interpreted as time-reversible infinitesimal rotations. Mass and energy positivity are trivially preserved. Finally, 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 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. – This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award no. DE-FG02-95ER54309. [1] F.D. Halpern and R.E. Waltz, Phys. Plasmas 25, 060703 (2018); F.D. Halpern and R.E. Waltz, A family of consistent and numerically stable fluid plasma models (to be submitted).

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