Numerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale terms

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present a numerical method based on an Eulerian approach to solve the Vlasov-Poisson system for 4D drift kinetic turbulence. Our numerical approach uses a conservative formulation with high-order (fourth and higher) evaluation of the numerical fluxes coupled with a fourth-order accurate Poisson solver. The fluxes are computed using a low-dissipation high-order upwind differencing method or a tuned high-resolution finite difference method with no numerical dissipation. Numerical results are presented for the case of imposed ion temperature and density gradients. Different forms of controlled regularization to achieve a well-posed system are used to obtain convergent resolved simulations. The regularization of the equations is achieved by means of a simple collisional model, by inclusion of an ad-hoc hyperviscosity or artificial viscosity term or by implicit dissipation in upwind schemes. Comparisons between the various methods and regularizations are presented. We apply a filtering formalism to the Vlasov equation and derive sub-grid-scale (SGS) terms analogous to the Reynolds stress terms in hydrodynamic turbulence. We present a priori quantifications of these SGS terms in resolved simulations of drift-kinetic turbulence by applying a sharp filter. © 2012 IOP Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)014004
JournalComputational Science & Discovery
Volume5
Issue number1
DOIs
StatePublished - Jun 12 2012

ASJC Scopus subject areas

  • Computational Mathematics
  • Numerical Analysis

Fingerprint

Dive into the research topics of 'Numerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale terms'. Together they form a unique fingerprint.

Cite this