Assessment of some high-order finite difference schemes on the scalar conservation law with periodical conditions
Journal Title: INCAS BULLETIN - Year 2016, Vol 8, Issue 4
Abstract
Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD) in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.
Authors and Affiliations
Alina BOGOI, Dragos ISVORANU, Sterian DANAILA
Keywords
Related Articles
- EP ID EP249356
- DOI 10.13111/2066-8201.2016.8.4.7
- Views 59
- Downloads 0
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