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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11 Citaten (Scopus)
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Samenvatting

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.
Originele taal-2Engels
Pagina's (van-tot)229-243
TijdschriftJournal of Computational and Applied Mathematics
Volume250
DOI's
StatusGepubliceerd - 2013

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