English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Maintaining conservation laws in the fully discrete setting is critical foraccurate long-time behavior of numerical simulations and requires accountingfor discrete conservation properties in both space and time. This paper derivesarbitrary order finite element exterior calculus spatial discretizations forthe two-dimensional (2D) Navier-Stokes and drift-reduced magnetohydrodynamicequations that conserve both energy and enstrophy to machine precision whencoupled with generally symplectic time-integration methods. Both continuous anddiscontinuous-Galerkin (DG) weak formulations can ensure conservation, but onlygenerally symplectic time integration methods, such as the implicit midpointmethod, permit exact conservation in time. Moreover, the symplectic implicitmidpoint method yields an order of magnitude speedup over explicit schemes. Themethods are implemented using the MFEM library and the solutions are verifiedfor an extensive suite of 2D neutral fluid turbulence test problems. Numericalsolutions are verified via comparison to a semi-analytic linear eigensolver aswell as to the finite difference Global Drift Ballooning (GDB) code. However,it is found that turbulent simulations that conserve both energy and enstrophytend to have too much power at high wavenumber and that this part of thespectrum should be controlled by reintroducing artificial dissipation. The DGformulation allows upwinding of the advection operator which dissipatesenstrophy while still maintaining conservation of energy. Coupling upwinded DGwith implicit symplectic integration appears to offer the best compromise ofallowing mid-range wavenumbers to reach the appropriate amplitude while stillcontrolling the high-wavenumber part of the spectrum.

Arbitrary Order Energy and Enstrophy Conserving Finite Element Methods for 2D Incompressible Fluid Dynamics and Drift-Reduced Magnetohydrodynamics