冲击波强间断的高分辨率低耗散的精确捕捉数值计算方法

The impact problem attracts considerable attention in the field of national defense and security. One major problem of the numerical simulation is accurately capturing and tracking strong discontinuities. Thus, it is necessary to develop a high-resolution and low-dissipation numerical calculation method. In this paper, we improved the traditional fifth-order weighted essential nonoscillating (WENO) scheme and proposed a high-resolution and low-dissipation WENO scheme. A local smooth indicator with a compact form was introduced to quantitatively characterize the smoothness of the subtemplates, making scaling formats to higher levels easier. Furthermore, we developed a new global indicator to measure the overall smoothness of the template, which can substantially reduce dissipation near the strong discontinuity. Compared with the traditional one, the new global indicator contains more complete information, which is one of the elements for improving the resolution. The complete information is important for improving the resolution; however, it is usually underestimated in a relatively rough zone with no discontinuity. The resolution of the scheme can be considerably improved if their contribution to the reconstruction flux is correctly increased while avoiding amplifying spurious numerical oscillations. The contribution of such relatively rough templates is governed by the coefficient of a weight expression term. It is empirically determined and constrained by the grid step size in traditional formats. As a result, an adaptive regulatory component in the weight is presented, which can automatically modify the weight with changes in the flow field and eliminate the dependence on the grid step size. This improvement is another element for improving the resolution. Finally, several typical numerical tests demonstrated that the new method can considerably reduce the dissipation near the discontinuity and improve the resolution of the classic WENO scheme. This advantage is particularly evident in the capture of vortices.