Summary
Several high resolution non-oscillatory discretization schemes have been formulated in a finite volume framework for the solution of Euler equations in order to compute inviscid transonic flow fields past airfoils. The theory is based on the local extremum diminishing (LED) principle, initially proposed by Jameson [12], [13] in 1993 for nonlinear scalar conservation laws. Higher order non-oscillatory schemes satisfying the LED criterion have been generated by using a suitable switching function and also by the use of flux limiters. For the implementation of these schemes to the solution of a system of conservation laws, a number of flux splitting techniques have been considered in the present work. Extensive numerical experiments indicate that the flux limited dissipation schemes, viz. the SLIP and USLIP schemes hold the promise of improving the accuracy of the results. The switched scheme with different types of flux splitting has also proved successful in the resolution of shock waves without oscillation.
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Ghosh, S., Niyogi, P. A study of non-oscillatory schemes based on LED principle for inviscid flow computation past airfoils. Acta Mechanica 139, 73–90 (2000). https://doi.org/10.1007/BF01170183
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DOI: https://doi.org/10.1007/BF01170183