强间断多介质流的高精度伪弧长方法

High-Order Pseudo Arc-Length Method for Strongly Discontinuity of Multi-Medium Flows

考虑到双曲守恒律方程随着时间的发展,产生的解会包含强间断.伪弧长算法可以削弱方程的奇异性,因此结合伪弧长算法和高精度权基本无振荡格式发展了高阶伪弧长算法,有效提高计算求解的精度和分辨率.由于在变形的网格中直接构造高精度格式较为复杂,因此通过坐标变换将控制方程映射至正交均匀的弧长空间,然后在弧长空间中完成计算.结合Level Set技术和虚拟流体法界面处理,将算法拓展到多介质流的计算中,针对网格移动以后Level Set距离函数的插值,提出了三阶非守恒插值格式.计算结果表明,高精度伪弧长算法具有较高的收敛阶,可以有效降低间断处的数值震荡,提高间断分辨率.

Considering the strong discontinuities appeared in the solutions of hyperbolic conservation law equations with the development of time and the ability of pseudo arc-length method(PALM)in weakening the singularity of the equation,a high-order PALM was developed based on the combination of the PALM and the highorder weighted essentially non-oscillatory(WENO)scheme to effectively improve the accuracy and resolution of the calculation.To overcome the complexity of a high-order scheme construction in the deformed mesh,a coordinate transformation method was adopted to make the governing equation mapped to the orthogonal uniform arc-length space,completing the calculation in the arc-length space.Combined with Level Set technology and real ghost fluid method(RGFM)interface processing,the algorithm was extended to the calculation of multi-medium flows.For the interpolation of Level Set distance function after grid movement,a third-order non-conservative interpolation scheme was proposed.The results show that the high-order PALM has high convergence order,which can effectively reduce the numerical oscillation at the discontinuity and improve the discontinuity resolution.