Higher Order Eno Scheme Applied Research

In this paper, we develop the high-order accurate essentially non-oscillatory (ENO) schemes on one and two-dimensional structured meshes in the finite volume formulation, and discuss their applications in hyperbolic conservation laws. ENO schemes are based on the approximation theory, which achieve high-order spatial accuracy by reconstructing piecewise smooth high-order approximate polynomial from the cell-averaging values. During the reconstruction, adaptive stencil technology, which automatically chooses the relatively smoothest stencil from all possible stencils, is adopted to guarantee essentially non-oscillation near the discontinuity. Thus, the ENO schemes have better shock-capturing ability. In the finite volume discretization approach, third-order TVD Runge-Kutta time stepping scheme is applied to the time integration, which assures the ENO schemes can be used in the high-order numerical simulation of unsteady flows. The numerical examples presented here are representative test cases of the aerodynamics problems which contains shock and complicated flow structures. The solutions of Euler equations for these examples certify the advantages of ENO schemes...