A family of high order targeted ENO scheme for compressible fluid simulations

Though classical WENO schemes achieve great success and are widely accepted, they show several shortcomings, such as too dissipative for reproducing turbulence and lack of numerical robustness with very high-order, in practical complex simulations. In this paper, we propose a family of high-order targeted ENO schemes for highly compressible fluid simulations involving wide range of sales. In order to increase the robustness of the very high-order classical WENO schemes, the reconstruction is built up by dynamically assembling a set of low-order upwind biased candidate stencils with incrementally increasing widths. Strong scale-separation formulations are proposed to extract the discontinuities from high wave-number physical fluctuations effectively. Coupled with a sharp cut-off technique, one candidate stencil is abandoned only on the condition that it is crossed by strong discontinuities, otherwise always applied with optimal standard weight. The background linear scheme is optimized with the constrain of preserving the approximate dispersion-dissipation condition. While such optimization leads to one-order degeneration, it provides favorable spectral property for intermediate and high wave-number region. By means of quasi-linear analyses and practical numerical experiments, a set of generally case-independent parameters are determined. The formulations of arbitrary high-order schemes are presented in a straightforward way. Five-point and six-point stencil schemes are further designed and analyzed in detail-s. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well established classical WENO schemes, present schemes suggest much improved property of robustness, low numerical dissipation in transition region and sharp discontinuity-capturing capacity, therefore are promising for DNS and LES of shock-turbulence interactions.