Third Order ENO Scheme on Non-Uniform Grid for Supersonic Flows

Yekaterina Moisseyeva; Altynshash Naimanova; Yerzhan Belyayev; Nurtoleu Shakhan

doi:10.4028/www.scientific.net/AMM.789-790.330

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 789-790Third Order ENO Scheme on Non-Uniform Grid for...

Third Order ENO Scheme on Non-Uniform Grid for Supersonic Flows

Abstract:

In the present paper the third order finite-difference shock-capturing essentially non-oscillatory (ENO) scheme for a non-uniform grid has been developed. The design of the ENO scheme is based on the methodology for uniform grids. To construct the essentially non-oscillatory piecewise polynomial, the Newtoninterpolant of the third order degree is adapted for the non-uniform grid. Also, the implementation of the symmetrical form of the slope limiters on non-uniform meshes is examined. The efficiency of the developed algorithm is demonstrated by the numerical experiments on the simulation of the three-dimensional turbulent steady flowfield generated by the transverse hydrogen injection into the supersonic air cross-flow. The comparison with results on the uniform grid using the coordinate system transformation is done.