Abstract
An assessment has been made of the character of the results near discontinuities yielded by selected numerical schemes of first-order (Rusanov and Van Leer schemes), second-order (Richtmyer and MacCormack schemes) and third-order (Rusanov scheme) and their capabilities are compared. The effectiveness of the Shuman Switch for use in higher order schemes has also been investigated. The Van Leer scheme is found to be preferable to the Rusanov scheme as it has a higher resolving power. The MacCormack scheme appears to behave better than the Richtmyer scheme in all aspects of shock handling. The Shuman switch is found to eliminate overshoots, undershoots and oscillations and fight nonlinear instabilities only by smearing the profiles. All schemes except the third order scheme produce artificial density profile near the wall when a shock wave is reflected from the wall.
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