论文标题
具有局部自适应耗散的有效靶向ENO方案，用于可压缩流量模拟
An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation
论文作者
论文摘要
可压缩流的高富度数值模拟需要使用数值方法具有稳定的冲击能力和高光谱分辨率。最近，制定了一个有针对性的基本非振荡（TENO）方案的家庭来满足此类要求。尽管Teno的流动流量非常低，但它引入了一个截止值$ C_T $，以维持非振荡性冲击捕获属性。 $ C_T $是问题取决于问题，因此需要通过反复试验来调整不同问题。由于$ c_t $实际上控制着Teno的耗散属性，因此选择$ C_T $的更好的冲击攻击能力总是意味着更高的耗散。为了克服这一点，在本文中，提出了一种本地自适应方法，以选择$ C_T $。通过基于WENO平滑度指示器引入一种新颖的自适应功能，$ c_t $是动态调整的表格$ 1.0 \ times 10.0^{ - 10} $，以降至$ 1.0 \ times 10.0 \ times 10.0^{ - 4} $，以更好地捕获根据记录模板的平滑度的震惊捕获。将新方法的数值结果与原始Teno方法和Teno-A方法的数值结果进行了比较（Fu等，JCP，2017年）。它表明，新方法能够更好地抑制不连续性附近的数值振荡，同时以较低的额外计算成本保持TenO的低耗散特性。
High fidelity numerical simulation of compressible flow requires the numerical method being used to have both stable shock-capturing capability and high spectral resolution. Recently, a family of Targeted Essentially Non-Oscillatory (TENO) schemes are developed to fulfill such requirements. Although TENO has very low dissipation for smooth flow, it introduces a cutoff value $C_T$ to maintain the non-oscillatory shock-capturing property. $C_T$ is problem depended and therefore needs adjustments by trial and error for different problems. As $C_T$ actually controls the dissipation property of TENO, the choice of $C_T$ for better shock-capturing capability always means higher dissipation. To overcome this, in this paper, a local adaptive method is proposed for the choice of $C_T$. By introducing a novel adaptive function based on the WENO smoothness indicators, $C_T$ is dynamically adjusted form $1.0 \times 10.0^{-10}$ for lower dissipation to $1.0 \times 10.0^{-4}$ for better capturing of shock according to the smoothness of the reconstruction stencil. Numerical results of the new method are compared with those of the original TENO method and the TENO-A method (Fu et al., JCP, 2017). It reveals that the new method is capable of better suppressing numerical oscillations near discontinuities while maintaining the low dissipation property of TENO at lower extra computational cost.
