论文标题
部分可观测时空混沌系统的无模型预测
A simple HLLE-type scheme for all Mach number flows
论文作者
论文摘要
为所有马赫数流提供了一个简单的HLLE型方案。在拟议的方案中，在HLLE方案中未添加额外的波结构来解决剪切波，而通过添加类似于HLLEM方案的波结构来解决接触波。剪切层的分辨率和低马赫数下的流量特征是通过基于面部正常马赫数的速度重建方法实现的。对数值不稳定性的鲁棒性是通过使用多维压力传感器在冲击附近的速度重建函数来实现的。通过渐近分析证明了所提出的方案解决低马赫流量特征的能力，而通过线性扰动和矩阵稳定性分析，证明了强烈冲击方案的稳定性。解决了一组数值测试用例，以表明所提出的方案在高速下没有数值冲击不稳定性问题，并且能够以非常低的马赫数字解决流量。
A simple HLLE-type scheme is proposed for all Mach number flows. In the proposed scheme, no extra wave structure is added in the HLLE scheme to resolve the shear wave while the contact wave is resolved by adding a wave structure similar to the HLLEM scheme. The resolution of the shear layers and the flow features at low Mach number are achieved by a velocity reconstruction method based on the face normal Mach number. Robustness against the numerical instabilities is achieved by scaling the velocity reconstruction function in the vicinity of shock with a multi-dimensional pressure sensor. The ability of the proposed scheme to resolve low Mach flow features is demonstrated through asymptotic analysis while stability of the proposed scheme for strong shock is demonstrated through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems at high speeds and is capable of resolving the flow features at very low Mach numbers.
