In this work, a novel hybrid weighted-compact-nonlinear scheme (WCNS) with fifth-order multi-resolution (MR) and low dissipation features is proposed to predict the one/two/three-dimensional (abbreviated as 1D/2D/3D) compressible discontinuous flows, which is motivated by three different state-of-the-art concepts (termed as “H-WCNS-s+”). For the improvements of present H-WCNS-s+: first-step, recently developed succinct local smoothing indicators (SIs) are introduced into the existing WCNS-MR scheme for reducing the computing cost and preserving fifth-order convergence (WCNS-MR-s); second-step, a new global SI is designed referring to an advanced Z-type SI which can result in lower numerical dissipation (H-WCNS-s-I); third-step, following adaptive stencils-selection concept in existing targeted essential non-oscillatory scheme, a new stencils-selection condition is designed to meet the feature of five-three-one center nested stencils, to improve the numerical stability near sharp discontinuity. Moreover, the numerical flux of Harten–Lax–van-Leer is mainly adopted in the present hybrid scheme. In the numerical experiments, first, the spectral properties of the proposed schemes are demonstrated and compared with other existing fifth-order schemes, and the numerical convergence rate of the proposed schemes are also illustrated, which has lower numerical dissipation than existing WCNS-type schemes. Subsequently, several 1D/2D classical or challenge compressible problems accompanied by different shock-wave phenomena (multi-small-scale, blast and implosion, etc.) are simulated to show the precision, robustness and shock-capturing capacity of the proposed schemes. Finally, the 3D compressible inviscid/viscous small-scale vortical structures are predicted to assess the extended capacity and virtue of the proposed scheme for 3D turbulent flow, comparing with other fifth-order WCNS-type schemes. Moreover, the comparisons of computing cost between the present new schemes and other WCNS-type schemes are also considered and discussed, to get that both of the proposed H-WCNS-s+ and WCNS-MR-s schemes have obviously lower computing cost than the existing MR WCNS-type schemes.
Huang et al. (Fri,) studied this question.