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首页> 外文期刊>Journal of Scientific Computing >Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme
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Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme

机译：四点模板的不连续性检测方法及其应用于开发三阶混合文艺方案

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摘要

First this paper analyzes the reason for the accuracy losing of the third-order weighted essentially non-oscillatory (WENO) scheme. It is shown that one reason is that the local smoothness indicators of the third-order WENO scheme cannot correctly treat the smooth three-point stencil containing a non-nodal critical point, here, 'non-nodal' means the critical point is not a grid point. And then a discontinuity-detecting method for a four-point stencil is proposed and applied to develop the high order accurate hybrid-WENO scheme by combining the third-order WENO scheme and a third-order upstream scheme. This four-point stencil is actually the stencil used for constructing the third-order WENO scheme (positive and negative numerical fluxes), hence the resulting hybrid-WENO scheme proposed by this paper does not introduce new grid point. Numerical examples show that the detecting method and the hybrid scheme are robust for problems with shocks, and the hybrid scheme obtains real third-order convergence rate for smooth solutions containing critical points.
机译：首先，本文分析了基本上非振荡（WENO）方案的三阶加权精度输失的原因。结果表明，一个原因是三阶WENO方案的局部平滑度指示器不能正确地治疗包含非节点临界点的光滑三点模板，这里“非节点”是指临界点不是一个网格点。然后提出了一种用于四点模板的不连续性检测方法，并应用通过组合三阶WENO方案和三阶上游方案来开发高阶精确的混合Weno方案。该四点模板实际上是用于构造三阶WENO方案（正负数量磁通量）的模板，因此本文提出的由此产生的混合Weno方案不会引入新的网格点。数值示例表明，检测方法和混合体方案对于冲击问题具有鲁棒，并且混合方案获得了含有关键点的平滑解决方案的实际三阶收敛速率。

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