Robust and Low-Dissipation Explicit Formulation of Improved Adaptive WCNS Scheme

In this paper, a novel adaptive central-upwind WCNS (weighted compact nonlinear scheme) based on an adjusting parameter of smoothness indicator is proposed. For the purpose of restraining numerical dissipation in smooth regions, avoiding spurious numerical oscillations dramatically, and preserving shock-capturing ability around discontinuity regions, an adaptive parameter is introduced in this modified WCNS scheme. Based on the above improvement, nonlinear weights could automatically fit discontinuity according to the local flow-field properties obtained by a discontinuity detector. In smooth regions, it is inclined toward optimal central scheme to minimize dissipations and capture turbulent features, while, in discontinuity regions, it is more likely inclined toward upwind scheme for stable shock-capturing ability and numerical robustness. Furthermore, to solve the problem of losing accuracy, the smoothness indicator with a mapping function is introduced. A variety of benchmark-test cases are tested to verify the modified WCNS scheme performance. Numerical results demonstrate that, compared with the EWENO-CU4 scheme, the modified WCNS scheme exhibits excellent shock-capturing ability, lower numerical dissipation, and higher numerical robustness in resolving complex flow features.