MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM
DOI:
https://doi.org/10.14311/AP.2021.61.0049Keywords:
Modified equation, finite difference, advection equationAbstract
This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods.
Downloads
References
R. J. LeVeque. Finite difference methods for ordinary and partial differential equations : steady-state and time-dependent problems. SIAM, 2007.
C. Hirsch. Numerical computation of internal and external flows, vol. 1,2. John Willey & Sons, 1988.
J. D. Anderson. Computational Techniques for Fluid Dynamics, vol. 1-2 of Springer Series in Computational Physics. Springer-Verlag Berlin Heidelberg, 2nd edn., 1991.
C. A. J. Fletcher. Computational Fluid Dynamics - The Basics with Applications. McGraw-Hill, 1995.
R. J. LeVeque. Numerical Methods for Conservation Laws. Lectures in Mathematics. Birkhäuser Verlag, 1990.
R. J. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2002.
R. Dvořák, K. Kozel. Mathematical modeling in aerodynamics (in Czech). Vydavatelství ČVUT, 1996.
R. Liska, B. Wendroff. Composite schemes for conservation laws. SIAM Journal on Numerical Analysis 35(6):2250–2271, 1998. doi:10.1137/S0036142996310976.
T. Bodnár, L. Beneš, K. Kozel. Numerical simulation of flow over barriers in complex terrain. Il Nuovo Cimento C 31(5–6):619–632, 2008. doi:10.1393/ncc/i2008-10323-4.
A. Sequeira, T. Bodnár. On the filtering of spurious oscillations in the numerical simulations of convection dominated problems. Vietnam Journal of Mathematics 47:851–864, 2019. doi:10.1007/s10013-019-00369-z.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Tomáš Bodnár
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
4. ddd
