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 and 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 and Discoveryen
kaust.authorSamtaney, Ravien
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