The Complete Flux Scheme : error analysis and application to plasma simulation

L. Liu; J. Dijk, van; J.H.M. Thije Boonkkamp, ten; D.B. Mihailova; J.J.A.M. Mullen, van der

doi:10.1016/j.cam.2013.03.011

The Complete Flux Scheme : error analysis and application to plasma simulation

L. Liu
, J. Dijk, van
, J.H.M. Thije Boonkkamp, ten
, D.B. Mihailova
, J.J.A.M. Mullen, van der

Research output: Contribution to journal › Article › Academic › peer-review

21 Citations (Scopus)

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Abstract

The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Péclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Péclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.

Original language	English
Pages (from-to)	229-243
Journal	Journal of Computational and Applied Mathematics
Volume	250
DOIs	https://doi.org/10.1016/j.cam.2013.03.011
Publication status	Published - 2013

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title = "The Complete Flux Scheme : error analysis and application to plasma simulation",

abstract = "The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid P{\'e}clet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid P{\'e}clet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.",

author = "L. Liu and \{Dijk, van\}, J. and \{Thije Boonkkamp, ten\}, J.H.M. and D.B. Mihailova and \{Mullen, van der\}, J.J.A.M.",

year = "2013",

doi = "10.1016/j.cam.2013.03.011",

language = "English",

volume = "250",

pages = "229--243",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

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T1 - The Complete Flux Scheme : error analysis and application to plasma simulation

AU - Liu, L.

AU - Dijk, van, J.

AU - Thije Boonkkamp, ten, J.H.M.

AU - Mihailova, D.B.

AU - Mullen, van der, J.J.A.M.

PY - 2013

Y1 - 2013

N2 - The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Péclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Péclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.

AB - The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Péclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Péclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.

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DO - 10.1016/j.cam.2013.03.011

M3 - Article

SN - 0377-0427

VL - 250

SP - 229

EP - 243

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

The Complete Flux Scheme : error analysis and application to plasma simulation

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