多介质五方程简化模型及界面捕捉的人工压缩算法

根据两介质五方程简化模型的基本假设,发展了适用于任意多种介质的体积分数方程。为了捕捉多介质界面,将HLLC-HLLCM混合型数值通量的计算格式推广应用于二维平面和柱几何的多介质复杂流动问题,在高阶精度的数据重构过程中采用斜率修正型人工压缩方法ACM。通过一维、二维多介质黎曼问题算例测试,结果表明：发展的计算格式能够较好地分辨接触间断和激波,间断附近物理量无振荡;对于添加了初始扰动的激波问题,能够有效抑制激波数值不稳定性;使用二维柱球SOD问题和接触间断型黎曼问题检验计算格式对多介质复杂流动问题的适应性。     

Rayleigh–Taylor instability at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability(RTI) of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.