摘要
基于代数重构思想,发展了一种新的双界面函数重构方法,并采用双正弦函数构造了双正弦界面重构方法(double sine interface capturing,DSINC).为验证不同界面函数对界面捕捉效果的影响,用数值方法求解了可压缩五方程模型,其中对流项的离散采用五阶WENO(weighted essentially non-oscillatory method)格式,时间积分采用三阶Runge--Kutta方法,通量计算分别考虑了HLL和HLLC方法,而状态方程采用Mie-Gr¨uneisen状态方程.在数值计算中,在界面附近,采用DSINC来获得体积分数的重构,而在远离界面的区域采用WENO格式来获得高阶插值状态.相比采用单界面函数的方法,如双曲正切界面重构方法(tangent of hyperbola for interface capturing,THINC),DSINC方法同样具有界面重构算法简单,在程序中添加方便等特点,两者区别在于,DSINC方法在重构过程中未知函数更易于求解,而无需求解复杂的非线性超越方程,这就使其具有易于向多维扩展的能力.一些典型的两相流动问题,如圆形水柱对流问题,两相三波点问题和激波-界面不稳定性问题等被用作不同界面函数对界面捕捉效果的影响对比.对比分析发现,DSINC与THINC在界面捕捉效果上大致保持一致,并在计算中表现出了较好的稳定性.双界面函数重构思想可以为多相流动界面的代数重构提供了一种新的思路.
We describe a novel double-interface-function(DIF)reconstruction method for effcient numerical resolution of a compressible two-phase flow.Based on the new method,double sine interface capturing scheme(DSINC)is obtained.Five-equation model is solved to analyze the effect of di_erent interface functions such as DIF and Single Interface function(SIF)on the interfaces captured numerically.Near the interfaces,the algorithm uses the DIF or SIF as a basis for the reconstruction of a sub-grid discontinuity of volume fractions.In regions away from the interfaces,WENO is used to reconstruct the convective term,and time integration of the algorithm is done by employing the TVD Runge-Kutta method.Comparing with tangent of hyperbola for interface capturing(THINC)using SIF method,the left and right states reconstructed by DSINC is simpler and we need not solve a transcendental equation.Numerical results are shown with the Mie-Gr¨uneisen equation of state(EOS)for sample problems such as discontinuous advection,two-phase triple problem and shock-bubble interaction problem with THINC and DSINC.It can be found that DSINC is able to get as effcient resolution interface as THINC and shows to be more stable in the simulation.
作者
李康
刘娜
何志伟
骆龙山
田保林
Li Kang;Liu Na;He Zhiwei;Luo Longshan;Tian Baolin(Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China)
出处
《力学学报》
EI
CSCD
北大核心
2017年第6期1290-1300,共11页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(11472059
U1630247
1730111)
