基于解析控制面预报船舶在波浪中航行载荷及大幅运动的多域法研究

The present project aims at developing a brand-new multi-domain boundary integral method. By introducing an analytical control surface, the fluid domain is divided into external and internal domains. The methods based on free-surface Green function and Rankine source function are coupled. The mathematical model for the multi-domain method is established, and a series of mathematical and physical analysis is conducted according to the features in external and internal domains. ..On the control surface in the form of a vertical circular cylinder, the Fourier-Laguerre expansions are used to express the velocity potential and its radial derivative. In the external domain, the Green function satisfying the free-surface boundary condition is used yielding the boundary integral equation (BIE) on the control surface, and asymptotic analysis of the integral of Green function is carried out to enhance computational efficiency. The BIE describes then the Dirichlet-to-Neumann (DtN) relationship between velocity potential and its radial derivative. In the internal domain limited by the hull surface, control surface and part of free surface in between, the Rankine source method is used to satisfy the nonlinear body boundary condition to account for large-amplitude motion of the hull. The complete BIE in the internal domain includes the DtN matrix through the continuous conditions on the control surface...Based on the Stokes theorem, middle-field formulation is developed for the computation of wave resistance and second-order wave-added resistance. Verifications with analytical solutions are performed for the external and internal solutions independently. The complete multi-domain solutions are validated against with existing numerical results and measurements of model tests. Finally, an accurate and reliable method is developed to predict wave loads and wave-induced motions of vessels operating in a seaway.

本项目研究一种新的多域边界积分法，采用解析控制面将流域分成內外域，将格林函数和Rankine源结合。建立多域法数学模型，根据内外域特点开展一系列开创性数理分析。在圆柱形控制面上将速度势和法向导数表达为Fourier-Laguerre级数。外域采用格林函数为基本解，建立控制面和水线上的边界积分方程；对格林函数的积分开展渐近分析。外域积分方程给出控制面上速度势和法向导数间关系，即DtN算子。內域包括船体表面、控制面及两者之间自由面，采用Rankine源为基本解，船体表面满足非线性物面条件，以考虑船体大幅运动。建立內域积分方程时，采用DtN算子得到完整方程组。利用Stokes定理，发展计算兴波阻力和二阶波浪增阻中场公式。为确保方法可靠有效，对内外域解分别验证。通过多域法得到的最终解与已存在的数值和试验结果及所开展的模型试验进行对比。最终形成一个精确可靠为预报船舶波浪载荷和波浪诱导运动的计算方法。

船舶运动响应和波浪载荷的预报关乎着船舶的安全，因此如何精确地预报船舶在波浪中航行的运动响应和波浪载荷是一个亟需研究的重要问题。本项目研究了一种新的多域边界积分法，采用了解析控制面将流域分成内外域，将格林函数和Rankine源结合。建立了多域法数学模型，根据内外域特点开展一系列开创性数理分析。在圆柱形控制面上将速度势和法向导数表达为Fourier-Laguerre级数。外域采用格林函数为基本解，建立了控制面和水线上的边界积分方程；对格林函数的积分开展渐近分析。外域积分方程给出控制面上速度势和法向导数间关系，即DtN算子。内域包括船体表面、控制面及两者之间自由面，采用Rankine源为基本解，船体表面满足非线性物面条件，以考虑船体大幅运动。建立了内域积分方程时，采用DtN算子得到完整方程组。利用Stokes定理，发展了计算兴波阻力和二阶波浪增阻中场公式。为确保方法可靠有效，对内外域解分别进行了验证。通过多域法得到的最终解与已存在的数值和试验结果及所开展的模型试验进行了对比。最终形成了一个精确可靠为预报船舶波浪载荷和波浪诱导运动的计算方法。