满足几何守恒律的WENO格式及其应用

A WENO scheme with geometric conservation law and its application

对几何守恒律的来源进行了分析,发展了一种满足几何守恒律的WENO格式,并应用于翼型层流分离现象的数值模拟中。为消除网格质量影响,采用守恒型方法计算网格导数,并将标准的WENO格式分解为中心差分部分和数值耗散部分。算例计算结果表明,几何守恒律对高精度有限差分WENO格式计算结果具有重要影响,本文方法能够消除网格导数计算误差,保证来流保持性。将本文方法应用于SD7003翼型层流分离现象的数值模拟中,计算结果与文献中计算及试验数据吻合较好,同时能够精细捕捉小尺度流场结构,准确模拟翼型层流分离现象中的复杂流动过程。

The origin of geometric conservation law is investigated,and a WENO scheme with geometric conservation law is developed. Then the scheme is applied to the simulation of flow past airfoils. In order to eliminate the influence of grid quality,the standard WENO scheme is divided into two part:a consistent central difference part and a numerical dissipation part,and the conservative metric method is implemented. Results of numerical tests show that the geometric conservation law plays a very important role in high order finite difference WENO scheme,and the developed scheme can eliminate the errors of metric derivatives and preserve the freestream preservation perfectly. Then the scheme is applied to the large eddy simulation of laminar separation phenomenon on the SD7003 airfoil. The computed results match well with the computational and experimental ones from some other papers. Besides,the present method has the characteristics of high order of accuracy and high resolution in capturing small-scale flow structures,and achieves good performance effect in predicting the formation of a laminar separation bubble and its subsequent burst and transition to turbulent structures.