The improvement of the mixing of the injected jet fuel in the cross‐flow oxidant (jet in cross‐flow (JICF)) in the scramjet combustor is still remains opened problem. JICF is accompanied with the formation of shock structures and leads to the shock wave boundary layer interactions (SWBLI) at the walls of the combustion chamber. The purpose of this paper is to study the influence of the interaction of the bow shock wave with the upper boundary layer and shock wave (reflected from the upper wall) with lower surface flow behind the jet on the mixture layer mechanism. For that, the numerical simulation of a supersonic flow with a transverse multispecies jet injection from the bottom wall of the plane channel with variations of the channel heights and the jet pressure ratio is done. The multispecies supersonic gas flow in a planar channel with perpendicular jet injection is numerically simulated. The Favre‐averaged Navier‐Stokes equations coupled with the k‐ω turbulence model are solved using the fourth order weighted essentially non‐oscillatory (WENO)‐scheme. The simulation correctly captured the main flow features near the jet and the comparison with the experimental data shows a satisfactory agreement. The reflected shock wave, formed as a result of the interaction of a bow shock wave with the boundary layer (SWBLI), reaches the lower boundary layer behind the jet and interacts with them. The numerical experiments reveal show that this shock/wave interaction causes an oscillation of the flow. The channel height variations show that with a decrease of the height the mixing rate increased.

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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.