Development of practical numerical methods for free surface flow

L)研究了由普通图像处理得到的破碎波过程的速度空间发散，以澄清质量守恒定律在多大程度上有效。结果表明，在底部和自由面附近，质量守恒定律较难满足。在此基础上，利用质量相容模型提出了一种满足质量守恒定律的速度修正方法。断路器的类型(通常由外部因素判断)、底坡和入射波条件可由存在或不存在复杂旋转运动的内部特性确定。2)数值方法采用边界拟合坐标(BFC)方法，该方法由边界拟合坐标和数值网格生成技术组成。通过对均匀坡度下沉式断路器的计算，验证了该方法的准确性。数值方法与断路器前的LDV和图像处理的实验结果的比较证实了数值方法的有效性。3)提出了一种既能提高自由表面识别精度又能满足质量守恒的计算方法。此外，由于采用密度函数的平流方程来跟踪自由面平流，因此必须考虑一种数值扩散较少的计算格式。对传统数值格式中数值扩散的研究表明，与数字化子方法(密度函数的切线变换)相结合的三次内插伪质点(CIP)方法扩散较小。

l) The spatial divergence of velocities obtained by ordinary image processing for the breaking wave process is investigated to clarify the extent to which the mass conservation law is valid. It was found that the mass conservation law is more difficult to satisfy near the bottom and the free surface. A velocity correcting method which satisfies the mass conservation law by using a mass-consistent model was thus proposed. Breaker types (which axe judged conventionally by external factors), bottom slope and incident wave condition, can be determined by the internal characteristics with or without existing complex rotational motions.2) The numerical method used the Boundary-Fitted Coordinate (BFC) method consisting of the Boundary-Fitted Coordinates and Numerical Grid Generation technique. The accuracy of the present method was examined by performing calculations for a plunging breaker on a uniform slope. A comparison of both the numerical method and the experimental results from LDV and image processing immediately before the breaker confirmed the validity of the numerical method.3) A computational technique for improving the accuracy of both recognizing the free surface and satisfying mass-conservation in The Volume of Fluid (VOF) method is presented. Furthermore, because the advective equation of density functions is used for tracking free surface advection, a computational scheme having less numerical diffusion must be considered. Investigations of numerical diffusion in conventional numerical schemes indicated that the Cubic Interpolated Pseudo-particle (CIP) method associated with the Digitizer method (tangential transformation of density functions) is less diffusive.