EPIC: The Elliptical Parcel-In-Cell method

The stability of inviscid Beltrami flow between parallel free-slip impermeable boundaries

“…In the near future, we will implement the present numerical method in a hybrid Eulerian–Lagrangian code for simulating inviscid, incompressible, rotating density-stratified flows, extending the 2-D code developed by Frey et al. (2022). This hybrid code will make use of space-filling, subgrid-scale ellipsoidal parcels to represent all dynamical (prognostic) variables, and will avoid the need for hyperdiffusion.…”

“…Hyperdiffusion is, however, not benign, and has some undesirable features such as non-monotonicity, particularly for high-order forms with (for further discussion, see Frey et al. 2022, and references therein).…”

“…The characteristic vorticity is computed as in Frey et al. (2022) but for 3-D flows. The time dependence allows the damping to adjust to the flow dynamically, rather than excessively damp in periods where there is little activity.…”

“…Finally, ω char = ω L2 /ω L1 . As argued in Frey et al (2022), this measure of a characteristic vorticity is designed to handle situations where intense vorticity is distributed sparsely in the domain, a common situation in a turbulent flow.…”

“…A common expedient used to control the energy cascade and prevent the build up of energy at the grid scale is to add hyperdiffusion to the evolution equations, since this permits one to mostly limit the numerical damping to small scales, compared to ordinary (molecular) diffusion (for a discussion, see Frey, Dritschel & Böing 2022). However, the presence of free-slip boundaries requires additional boundary conditions for consistency (Jones & Roberts 2005).…”