In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the Gradient-Based Reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor-Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow.

翻译：本文提出了一种新颖的选择性间断传感器方法，用于可压缩Navier-Stokes方程的数值模拟。鉴于向特征空间转换已是降低单元界面插值过程中高频振荡的常用手段，我们利用Euler方程的特征波结构，对构成该方程的各种波进行选择性处理。该方法采用Ducros激波感知准则来检测并抑制激波引起的振荡，同时应用不同准则来检测并抑制接触间断引起的振荡。此外，该方法具有普适性，可应用于任何采用特征变换和激波传感器的计算方案。然而，本文重点针对基于梯度重构（Gradient-Based Reconstruction）的格式族展开研究。我们进行了一系列包含多种间断类型的无粘与有粘算例测试。结果表明，所提方法能显著减少因不当处理各类间断（例如在存在强接触间断的流场中直接应用Ducros激波传感器）而产生的高频振荡。此外，与基础Ducros传感器相比，所提方法在泰勒-格林涡模拟中预测的体平均动能和涡量分布曲线相似，表明当流场中不存在接触间断时，该方法不会引入不必要的数值耗散。