Numerical dissipation control in an adaptive WCNS with a new smoothness indicator

A novel adaptive central-upwind weighted compact nonlinear scheme (WCNS) based on an adjusting parameter of the smoothness indicator is proposed. For the purposes of restraining numerical dissipation in smooth regions, preserving shock-capturing ability and avoiding spurious numerical oscillations around discontinuous regions, an adaptive parameter is introduced in this improved WCNS. The improved scheme can automatically modify the adaptive parameter to fit nonlinear weights to discontinuity according to the local flow-field properties obtained by a discontinuity detector. In smooth regions, the scheme inclines to an optimal central scheme to minimize dissipations and capture turbulent features. While, in discontinue regions, it is more likely to behave as an up-wind scheme for stable shock-capturing ability and numerical robustness. Furthermore, to solve the problem of losing accuracy, a smoothness indicator with a mapping function is introduced. The order-recover property of the improved scheme can obviously avoid unsymmetrical breaking of the flow field. A variety of benchmark cases are tested to verify the improved WCNS performance. The computational efficiencies of all cases have been estimated by measuring the computational time. Numerical results demonstrate that the improved WCNS exhibits excellent shock-capturing ability, lower numerical dissipation, higher numerical robustness and efficiency in resolving complex flow features.