Finite spectral essentially non-oscillatory scheme

In this paper a new finite spectral essentially non-oscillatory (FSENO) scheme is proposed for treating discontinuities in computational fluid dynamics. The new scheme is based on the finite spectral method and the idea of essentially non-oscillatory (ENO). Uniform high-order accuracy in smooth regions of solutions and sharp capturing of shock waves and other discontinuities are achieved by using it. We present numerical results for various one-dimensional Euler equations including Sod's and Lax's test problems. Finally, we simulate a turbulent flow compressed by a shock wave and a two-dimensional detonation.