直接边界元法解势流速度场问题

在船舶水动力学中,大多采用以Hess-Smith方法为基础的间接边界元法求解势流绕流问题,但Hess-Smith方法本质上是基于物理直观提出,在理论和数值计算上都存在着缺点。直接边界元法虽然在船舶水动力领域有着非常广阔的应用前景,但至今应用较少。为推广直接边界元法在船舶水动力学中的应用,根据边界积分法建立积分方程,采用直接边界元法对无界势流绕流问题予以求解,得出流场速度势和物面上的速度分布,并通过与解析解的比较进行误差分析。对二维、三维问题的算例进行数值计算。数值计算过程用Matlab编程实现。结果表明:直接边界元法在求解船舶势流绕流问题中具有足够的精度和较高的效率,且数值计算实现过程更简洁,可发展成为求解船舶兴波等船舶水动力学问题的通用方法。

Direct Boundary Element Method for the Problem of Potential Flow Velocity Field

In the field of ship hydrodynamics, scholars usually adopt Hess - Smith method to solve the potential flow problem. However, this method is essentially based on the physical intuition, and there are shortcomings concerning this theory in numerical calculation. Since the direct boundary element method is rarely used in ship hydrodynamic problems, the presented method in this paper has broad application prospects in the field of ship hydrodynamics and may promote the direct boundary element method. According to the boundary integral method, an integral equation is established to solve the unbounded potential flow problem, and the flow field velocity distribution on the surface of the velocity potential is then obtained. A comparison with the analytical solution is finally conducted for error analysis. In this paper, both 2D and 3D numerical examples are provided and programmed to realize the numerical calculation process in Matlab. The results show that the direct boundary element method has decent precision and efficiency, and the numerical implementation is even more concise. Moreover, this method can be developed into general forms to solve other ship dynamic problems.