论文标题
一种构建高准确且健壮的WENO-Z型方案的新方法
A novel method for constructing high accurate and robust WENO-Z type scheme
论文作者
论文摘要
本文提出了一种构建坚固且高阶准确加权基本上非振荡（WENO）方案的新方法。 The method is mainly based on the WENO-Z type scheme, in which, an eighth-order global smoothness indicator (the square of the approximation of the fourth-order derivative on the five-point stencil used by the fifth-order WENO scheme) is used, and in order to keep the ENO property and robustness, the constant 1 used to calculate the un-normalized weights is replaced by a function of local smoothness indicators of candidate sub-stencils.该功能旨在具有以下自适应属性：如果五点模板包含不连续性，则该功能接近一个小值，否则，它将接近大价值。分析和数值结果表明，所得的WENO-Z类型（WENO-ZN）方案对于捕获冲击波是可靠的，并且在平滑区域中，在一阶关键点上达到了五阶准确性，在二阶关键点处可以达到第四阶准确度。
A novel method for constructing robust and high-order accurate weighted essentially non-oscillatory (WENO) scheme is proposed in this paper. The method is mainly based on the WENO-Z type scheme, in which, an eighth-order global smoothness indicator (the square of the approximation of the fourth-order derivative on the five-point stencil used by the fifth-order WENO scheme) is used, and in order to keep the ENO property and robustness, the constant 1 used to calculate the un-normalized weights is replaced by a function of local smoothness indicators of candidate sub-stencils. This function is designed to have following adaptive property: if the five-point stencil contains a discontinuity, then the function approaches to a small value, otherwise, it approaches to a large value. Analysis and numerical results show that the resulted WENO-Z type (WENO-ZN) scheme is robust for capturing shock waves and, in smooth regions, achieves fifth-order accuracy at first-order critical point and fourth-order accuracy at second-order critical point.
