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

Handle URI:
http://hdl.handle.net/10754/562053
Title:
Numerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale terms
Authors:
Samtaney, Ravi ( 0000-0002-4702-6473 )
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.
KAUST Department:
Applied Mathematics and Computational Science Program; Mechanical Engineering Program; Physical Sciences and Engineering (PSE) Division; Clean Combustion Research Center; Fluid and Plasma Simulation Group (FPS)
Publisher:
IOP Publishing
Journal:
Computational Science & Discovery
Issue Date:
1-Jan-2012
DOI:
10.1088/1749-4699/5/1/014004
Type:
Article
ISSN:
17494680
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program; Clean Combustion Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorSamtaney, Ravien
dc.date.accessioned2015-08-03T09:43:40Zen
dc.date.available2015-08-03T09:43:40Zen
dc.date.issued2012-01-01en
dc.identifier.issn17494680en
dc.identifier.doi10.1088/1749-4699/5/1/014004en
dc.identifier.urihttp://hdl.handle.net/10754/562053en
dc.description.abstractWe 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.en
dc.publisherIOP Publishingen
dc.titleNumerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale termsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentClean Combustion Research Centeren
dc.contributor.departmentFluid and Plasma Simulation Group (FPS)en
dc.identifier.journalComputational Science & Discoveryen
kaust.authorSamtaney, Ravien
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