迎风格式在水滴欧拉方程数值求解中的应用

Application of Upwind Scheme in Numerical Solution of Euler Equation for Water Droplets

数值模拟是研究飞机结冰的重要手段,为获取水滴撞击特性,通常采用欧拉法求解水滴运动方程。液态水含量在空间分布上存在间断,会导致水滴欧拉方程的求解极易发散;若采用一阶格式,虽然稳定性得到提高,但计算精度难以保证满足工程设计需求;有研究者通过添加扩散项以提升收敛性,但会人为增加数值耗散。针对这一问题,本文采用一阶迎风格式对水滴欧拉方程的对流通量进行离散,并通过线性重构与限制器函数保证计算精度达到二阶,建立一种基于迎风离散格式的水滴欧拉方程二阶求解方法。通过对比NACA0012、NACA23012和NLF0414翼型水滴撞击特性计算结果与FENSAP-ICE软件的结果,验证了该方法的有效性与计算精度。

Numerical simulation is an important means to study aircraft icing.In order to obtain water droplet impingement characteristics,Euler method is usually used to solve the control equation of droplet movement.Due to the discontinuity in the spatial distribution of liquid water content,the solution of the Euler equation of water droplet is easily divergent.If the first-order format is adopted,although the stability is improved,the calculation accuracy is difficult to meet the engineering design requirements.Some researchers increase convergence by adding diffusion terms,but artificially increase numerical dissipation.To solve this problem,the convective flux of the water droplet Euler equation is discretized by a first-order upwind scheme,and the calculation accuracy is guaranteed to reach the second-order by linear reconstruction and limiter functions.The effectiveness and accuracy of the method are verified by comparing the calculation results of NACA0012 NACA23012 and NLF0414 airfoils droplet impingement characteristics with FENSAP-ICE software.