论文标题
WENO-Z型方案的一般改进
A general improvement in the WENO-Z-type schemes
论文作者
论文摘要
在[36]中，通过引入订单保留（OP）标准来设计了一种用于双曲线问题的新型有限体积WENO方案。在这项持续的工作中，我们将OP标准扩展到WENO-Z型方案。首先，我们从受广泛的数值观察启发的映射角度重写Z型权重的公式。应得的是，我们构建了本地订单保留（LOP）映射的概念，该映射是订单保存（OP）映射的扩展，并将改进的Weno-Z-Z-type方案表示为LOP-GMWENO-X。 LOP-GMWENO-X方案比现有的WENO-Z型方案优于四个主要优势。首先，新方案可以修改现有的WENO-Z型方案的严重缺点，这些方案大多数人都遭受了严重的虚假振荡或未能在长期计算不连续性问题的长期计算中获得高分辨率。其次，他们可以在长期输出时间以高阶临界点解决问题上保持相当高的分辨率。第三，他们显然可以通过高频但光滑的波浪获得更高的分辨率。最后，它们可以显着减少震动后振荡，以模拟某些具有强冲击波的2D问题。进行了广泛的基准示例，以说明这些优势。
A new type of finite volume WENO schemes for hyperbolic problems was devised in [36] by introducing the order-preserving (OP) criterion. In this continuing work, we extend the OP criterion to the WENO-Z-type schemes. We firstly rewrite the formulas of the Z-type weights in a uniform form from a mapping perspective inspired by extensive numerical observations. Accrodingly, we build the concept of the locally order-preserving (LOP) mapping which is an extension of the order-preserving (OP) mapping and the resultant improved WENO-Z-type schemes are denoted as LOP-GMWENO-X. There are four major advantages of the LOP-GMWENO-X schemes superior to the existing WENO-Z-type schemes. Firstly, the new schemes can amend the serious drawback of the existing WENO-Z-type schemes that most of them suffer from either producing severe spurious oscillations or failing to obtain high resolutions in long calculations of hyperbolic problems with discontinuities. Secondly, they can maintain considerably high resolutions on solving problems with high-order critical points at long output times. Thirdly, they can obtain evidently higher resolution in the region with high-frequency but smooth waves. Finally, they can significantly decrease the post-shock oscillations for simulations of some 2D problems with strong shock waves. Extensive benchmark examples are conducted to illustrate these advantages.
