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

Hiroshi Isshiki


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.


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

Full Text:



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.


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.


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


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

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


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


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


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.


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.



  • There are currently no refbacks.

Copyright (c)