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.