Diffraction–radiation of regular waves by a body such as an offshore structure or a moored ship is considered within the classical framework of potential-flow theory, which is commonly used because it is realistic and practical. A simple analysis that is based solely on straightforward applications of Green’s classical identity to a ‘free-waterplane’ flow-model and a ‘rigid-waterplane’ flow-model is expounded. These alternative flow-models and the related straightforward applications of Green’s identity yield an elementary yet rigorous justification of the practical and effective method, called ‘combined boundary integral equation method’ (CBIEM), of Lau and Hearn for preventing irregular frequencies. This method is shown to be significantly more efficient, and arguably simpler and more logical, than the widely-used extended boundary integral method of Lee and Newman. A modification of the ‘combined boundary integral equation method’ is also given. This modification involves a pair of boundary integral equations that are mathematically equivalent to the pair of integral equations solved in the CBIEM, but are weakly singular.

离岸结构或系泊船舶等物体的规则波的衍射辐射被认为是在势流理论的经典框架内，因为它是现实和实用的，所以被广泛使用。阐述了一个简单的分析，该分析完全基于格林经典恒等式对“自由水线”流模型和“刚性水线”流模型的直接应用。这些替代流动模型和格林恒等式的相关直接应用为 Lau 和 Hearn 用于防止不规则频率的实用有效方法（称为“组合边界积分方程法”（CBIEM））提供了基本而严格的证明。这种方法被证明更有效，可以说更简单，更合乎逻辑，比广泛使用的 Lee 和 Newman 的扩展边界积分方法。还给出了对“组合边界积分方程方法”的修改。这种修改涉及一对边界积分方程，它们是在数学上等同于在 CBIEM 中求解的一对积分方程，但它们是弱奇异的。