## 1 Introduction  
Large-scale offshore aquaculture farming has become a sustainable method of feeding the world, since the practice of farming the ocean is growing rapidly. However, potentially high-energy oceanic conditions such as strong currents can cause net deformation, significantly influencing the current forces on and oxygen levels inside the cages. Understanding the fluid-structure interactions supports the longevity of the systems and is, therefore, vitally important for designing offshore aquaculture cages. Research, including experimental studies and analytical/numerical predictions for estimating the fluid forces on nets, have been examined thoroughly [(1)]. According to their report, to numerically analyze the nets in currents and waves, a structure solution method, such as the finite element method [(2; 3; 4; 5; 6; 7; 8)]; a fluid solution method, such as computational fluid dynamics (CFD) method [(9; 10; 11; 12; 13; 14)]; and a coupled fluid-structure interactions (FSI) method [(15; 16; 17; 18)] have been established. Alongside these three methods, two hydrodynamic force models are suggested to calculate viscous forces on nets [(19)]. Dependent on how a net is approximated, the hydrodynamic force models can either be the Morison-type force model or the screen-type force model. The finite element method (FEM) focuses on the structural models. The net is modeled with triangular/truss elements or mass-spring systems. The hydrodynamic forces on the net are calculated based on the Morison equation or the screen-type force model. The Newton-Raphson and Rouge-Kutta approaches are used to solve the equations of motion. These FEM models are computationally efficient because they model the net in a mesh grouping manner without losing the geometrical and physical properties. However, a comparative study showed that FEM-based models over-predicted the drag force of the net [20]. One possible reason is that the interference of the flow field is not considered. Thus, further development of the numerical models is suggested. CFD-based numerical models such as the porous media model have been developed to examine the flow field and velocity distribution around and inside net cages. In the porous model, the net is approximated by a porous media sheet instead of an equivalent system of cylinders. Considering the fluid viscosity, the Reynolds-averaged Navier-Stokes (RANS) equations and turbulence models are used to ascertain the underlying fluid mechanisms. However, the porous media model is based on the Darcy-Forchheimer law and it requires the prescribed resistance coefficients. [PERSON] and [PERSON] [16] directly used free coefficients, namely the normal and tangential resistance coefficients, in porous media simulations by neglecting the Darcy-Forchheimer dependencies, since it was challenging to incorporate all aspects of the properties influencing the force on a net. Note that using a porous media model leads to a constant pressure-loss zone rather than a natural pressure drop. Moreover, the strategy used to resolve net deformation in the porous media model is likely the overset mesh, which leads to overlapped regions in the intersectional zones [16; 21]. These issues need to be addressed. FEM offers effective structural models, while a CFD-based porous media model facilitates the fluid field-analysis. Together, the structural model (e.g., lumped-mass model) and the porous media model have been used to examine the FSI between the fluid and the flexible nets [15]. This coupled FSI model takes net deformation into account using an iterative scheme. It assumes that a steady condition is satisfied at each iteration. Prompted by [PERSON] et al. [15], [PERSON] and [PERSON] [16] conducted an FSI analysis of an aquaculture net cage under steady flow using a coupled model, which combines the porous media model and the lumped-mass structural model. However, it seems that their model was unable to predict net twines' flow characteristics. Most recently, [PERSON] et al.