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基于势流理论，考虑流场的可压缩性，首先利用积分变换导得了势流问题的一个动力学倒易定理．在此基础上进而求得问题对应的时空边界积分方程．然后通过对边界和时间轴同时离散，建立了一组有递推形式的时间域边界元方程．最后结合液面条件和物体运动方程耦合求解得到了刚体的撞水响应．几个算例表明时域边界元法比普通边界元法有更高的计算效率．
Based on the potential flow theory, considering the compressibility of the flow field, a kinematic reciprocity theorem of potential flow problems is first derived by integral transformation. On this basis, the space-time boundary integral equation corresponding to the problem is obtained. Then a set of time-domain boundary element equations in recursive form are established by discretizing the boundary and the time axis at the same time. Finally, the bounder response of the rigid body is obtained by coupling the liquid surface condition and the object motion equation. Several examples show that the time domain boundary element method has higher computational efficiency than the ordinary boundary element method.