The complete flux scheme-Error analysis and application to plasma simulation

被引：17

作者：

Liu, L. ^{[1
]}

van Dijk, J. ^{[1
]}

Boonkkamp, J. H. M. ten Thije ^{[2
]}

Mihailova, D. B. ^{[1
]}

van der Mullen, J. J. A. M. ^{[1
]}

机构：

[1] Eindhoven Univ Technol, Dept Appl Phys, NL-5600 MB Eindhoven, Netherlands

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2013年 / 250卷

关键词：

Complete flux scheme; Exponential difference scheme; Error analysis; Plasma model; SINGULAR PERTURBATION PROBLEM; GLOW-DISCHARGES; MODEL;

D O I：

10.1016/j.cam.2013.03.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Peclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Peclet 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. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：229 / 243

页数：15

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