A Method for Reduction of Spurious or Numerical Oscillations in Integration of Unsteady Boundary Value Problem

Authors

  • Hiroshi Isshiki Saga University

Keywords:

Spurious or numerical oscillation, Central differencing, Diffuser by moving average, Burgers’ equation

Abstract

Elimination of the spurious or numerical oscillations is very important in the solution of unsteady boundary value problem by FDM. Upwind differencing in advection problem is very popular, but numerical diffusion is too big. Flux limiters are very effective to eliminate the numerical oscillations, but the procedure is rather complicated. In the present paper, a very simple and unique method is proposed to reduce numerical oscillations. The method is verified by numerical calculations. This solution can be applied to many problems and to other solutions such as FEM, BEM etc. This solution can be applied not only to explicit method but also to implicit method. This solution can be extended easily to multi-dimensional problems.

Author Biography

Hiroshi Isshiki, Saga University

IOES (Institute of Ocean Energy , Saga University)

Visiting professor

References

H. Isshiki, Improvement of Stability and Accuracy of Time-Evolution Equation by Implicit Integration, Asian Journal of Engineering and Technology (AJET), Vol. 2, No. 2 (2014), pp. 1339–160.

file:///C:/Users/l/Downloads/1205-5161-1-PB.pdf

P. Lax, B. Wendroff, Systems of conservation laws, Communications on Pure and Applied Mathematics, Vol. XIII (1960), pp. 217–237.

A. Harten, High Resolution Schemes for Hyperbolic Conservation LawsHigh resolution schemes using flux limiters, Journal of Computational Physics, 135 (1997), pp. 260–278, reprinted from Volume 49, Number 3, March (1983), pp. 357–393.

http://www.ece.uvic.ca/~bctill/papers/numacoust/Harten_1983.pdf

P.K. Sweby, High resolution schemes using flux limiters, SIAM J. NUMER. ANAL, Vol. 21. No. 5 (1984), pp. 995-1011.

http://www.rsmas.miami.edu/personal/miskandarani/Courses/MPO662/Sweby,Peter/FluxLimiters.SIAMv21-5.pdf

Wikipedia, Flux limiter, http://en.wikipedia.org/wiki/Flux_limiter.

J. Hudson, Numerical Techniques for Conservation Laws with Source Terms.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.224.7654&rep=rep1&type=pdf.

J. Hudson, Numerical Techniques for Morphodynamic Modelling, MSc dissertations - University of Reading, (2001).

http://www.reading.ac.uk/web/FILES/maths/J_hudson_thesis.pdf

J. Hudson, A Review on the Numerical Solution of the 1D Euler Equations, The University of Manchester, (2006).

http://www.reading.ac.uk/web/FILES/maths/J_hudson_thesis.pdf

Wikipedia, Burgers’ equation, http://en.wikipedia.org/wiki/Burgers'_equation.

J.D. Fletcher, Generating exact solutions of the two-dimensional Burgers’ equation, Int. J. Numer. Meth. Fluids, 3 (1983) pp. 213-216.

http://wudpeckerresearchjournals.org/RJPAS/pdf/2012/November/Alsaif%20and%20Abdul-Hussien.pdf

A.J.S. Al-Saif, A. Abdul-Husein, Generating exact solutions of two-dimensional Coupled Burgers’ equations by the first integral method, Research Journal of Physical and Applied Science, vol. 1(2) (2012) pp. 029-033.

http://wudpeckerresearchjournals.org/RJPAS/pdf/2012/November/Alsaif%20and%20Abdul-Hussien.pdf

Downloads

Published

2014-06-15

How to Cite

Isshiki, H. (2014). A Method for Reduction of Spurious or Numerical Oscillations in Integration of Unsteady Boundary Value Problem. Asian Journal of Engineering and Technology, 2(3). Retrieved from https://ajouronline.com/index.php/AJET/article/view/1360

Issue

Vol. 2 No. 3 (2014): June 2014

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • 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.
  • 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).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.