## Appendix A  
In light of the paper's brevity, the important theories are presented in the second section, and supplementary theories are presented within the confines of the Appendix A. This manuscript employs a viscous fluid model based on the RANS equation. The volume of the fluid domain (VOF) and k-\(\varepsilon\) turbulence models are utilized. The numerical simulations are conducted using a coupled approach for pressure and velocity. The free-liquid surface is tracked using the VOF method, where \(\alpha_{i}\) represents the phase volume fraction, \(V_{i}\) denotes the volume of phase \(i\) in the grid cell, and \(V\) represents the volume of the grid cell. \[\alpha_{i}=\frac{V_{i}}{V^{\prime}},\,\sum_{i=1}^{N}\alpha_{i}=1 \tag{1}\]where \(N\) is the total number of phases, \(\alpha_{i}=0\) means no phase \(i\) at all, and \(\alpha_{i}=1\) means completely phase \(i\). Moreover, \(0<\alpha_{i}<1\) means that there is an interface between the phases. The movement of multiple floating bodies results in relative translation and rotation. This dynamic behavior is elucidated by equations of motion and constraint equations of multifloating bodies:  
\[M\ddot{q}=f\] (A2)  
\[M= \begin{pmatrix}M_{1}&\cdots&0\\ \vdots&\ddots&\vdots\\ 0&\cdots&M_{n}\end{pmatrix} \] (A3)  
where \(q\) is the vector of generalized coordinates, \(f\) is a generalized force, and \(M\) is the block-diagonal matrix of the inertia matrices of the rigid bodies. Combining equations of motion with constraints:  
\[\phi(q,t)=0\] (A4)  
Constraints are expressed as linear conditions of body acceleration. Taking the second derivative of Equation (A4):  
\[J\ddot{q}=Q\] (A5)  
Among them, \(J\) is the Jacobian matrix of \(\phi\), \(\ddot{q}\) is the acceleration of the bodies, and \(Q\) is an inhomogeneity. A constraint force is added to the system. By introducing the Lagrangian multiplier (\(\lambda\)) of all the constraints, the workless constraint force is given by:  
\[f^{c}=J^{T}\cdot\lambda\] (A6)  
A vector (\(\lambda\)) is sought such that the constraint force (\(f^{c}\)) in combination with any external force (\(f^{ext}\)) produces a motion that satisfies the constraints, as given by Equation (A5). According to Equation (A6), Equation (A2) can be written as follows:  
\[M\ddot{q}=J^{T}\lambda+f^{ext}\] (A7)  
\[\ddot{q}=M^{-1}J^{T}\lambda+M^{-1}f^{ext}\] (A8)  
Generate the following system of linear equations:  
\[A\lambda=b\] (A9)  
where  
\[A=JM^{-1}J^{T}\] (A10)  
\[b=-JM^{-1}f^{ext}+Q\] (A11)  
\(\lambda\) is obtained through Equation (A9). When \(\lambda\) is known, Equation (A8) is integrated twice to yield the generalized coordinate vector. Salvaging sunken ships is a special mode of operation. Within this context, the entire salvage mechanism assumes a state of relative equilibrium. Hence, the cable module embedded within the framework of STAR-CCM+ chiefly encompasses elements of greater consequence to the steadiness of maritime undertakings, notably, cable rigidity and submerged mass. Additional variables, including hydrodynamic resistance, and fluid pressure, adhere to the default parameters designated for ordinary sea circumstances. For multifloating body coupled motions, the parameter equations of connecting cables between multifloating bodies are:  
\[x=au+bsinh(u)+\alpha\] (A12)\[y=acosh(u)+\frac{b}{2}sinh^{2}(u)+\beta,\text{ for }u_{1}\leq u\leq u \tag{113}\]  
where  
\[ \begin{array}{c}a=\frac{c}{\lambda_{0}g}\\ b=\frac{b!}{D_{Lq}}\\ c=\frac{\lambda_{0}\lambda_{0}\alpha g}{sinh(u_{2})-sinh(u_{1})}\end{array}  \tag{114}\]  
Among them, \(g\) is the gravitational acceleration and \(\lambda_{0}\) and \(L_{eq}\) are the mass per unit length and slack length of the cable, respectively. The stiffness of the cable is represented by \(D\), and the integral constants \(\alpha\) and \(\beta\) depend on the cable's initial and final connection points as well as its total mass. Forces \(f_{1}\) and \(f_{2}\) at the first and last ends of the cable are:  
\[ \begin{array}{c}f_{1,x}=c\\ f_{1,y}=csinh(u_{1})\end{array}  \tag{115}\]  
\[