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

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

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Abstract

The Complete Flux scheme (CFS) (J.H.M. ten Thije Boonkkamp et al., J. Sci. Comput. 46 (2011) 47–70) is an extension of the widely used exponential di¿erence scheme for advection-di¿usion-reaction equations. In the present 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 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 model system and a real-world model of a parallel-plate glow discharge. The results indicate that the usage of 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
Place of Publication	Eindhoven
Publisher	Technische Universiteit Eindhoven
Number of pages	22
Publication status	Published - 2012

Publication series

Name	CASA-report
Volume	1227
ISSN (Print)	0926-4507

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abstract = "The Complete Flux scheme (CFS) (J.H.M. ten Thije Boonkkamp et al., J. Sci. Comput. 46 (2011) 47–70) is an extension of the widely used exponential di¿erence scheme for advection-di¿usion-reaction equations. In the present 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 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 model system and a real-world model of a parallel-plate glow discharge. The results indicate that the usage of 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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AU - Mullen, van der, J.J.A.M.

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