楔形体入水时域解的复边界元数值分析

基于速度势理论,利用复数变量边界元法对二维楔形体常速入水冲击的时域解进行了数值研究。 以相似解作为数值计算的初始条件,采用时域解射流线性近似处理方法,利用复数变量边界元法进行求解,以 减少计算量和数值误差。深入讨论了扩展坐标系求时域解、射流处理、网格划分和网格更新等关键技术。最 后数值计算了不同斜升角楔形体入水时的自由液面隆起、射流飞溅和压力分布,经与相似解结果作比较,自由 液面隆起轮廓基本吻合,而压力分布更符合实际情况,从而证明了模型及分析方法的正确性。

Numerical analysis for water entry of wedges based ona complex variable boundary element method

The water entry problem of the 2-D wedge with a constant speed is numerically analyzed based on the velocity potential theory.A new jet linear approximation method is incorporated into the complex variable boundary element solver that describes the jet generated by the water entry of wedges to nearly simulate the free surface shape,jet and pressure distribution along the wetted area of the wedge contour.And the same time Cauchy integral theorem is used as the integration equation,and the similarity solution as the initial condition.Some important numerical techniques are discussed in detail such as time marching solution,jet treatment,grid mesh generation and the free surface deformation updating.Finally,the pressure distribution and wave elevation for the wedges with different deadrise angles are gotten.The proposed method is validated through comparisons with the similarity solution and good approximations are found.