Optimization algorithms are key approaches for enhancing hydrofoil performance inVertical Axis Wind/Water Turbines (VAWTs). These algorithms provide accurateresults at the cost of large training datasets. Given the high computational cost ofthe commonly applied RANS solvers, this study aims to explore the potential of morecomputationally efficient alternatives, specifically Quasi-steady Hydrofoil Theory(QHT) and the Unsteady Boundary Element Method (UBEM), through comparativeanalysis with SST k-ω Reynolds-averaged Navier-Stokes (RANS) simulations.QHT is derived from a classic hydrofoil theory for VAWT. According to the geometryand periodic motion of VAWT system, QHT formulates the relative inflow and angleof attack of the hydrofoil based on the azimuth angle, while disregarding the memoryand wake effect of the flow field. The torque performance is accessed based on thelift and drag coefficient from an external database (XFOIL), which depends on thehydrofoil type. Reduce frequency is reviewed to evaluate the performance of quasisteadyformulation, which measures the residence time of a particle convecting overthe hydrofoil chord compared to the period of motion. It is found that the reducedfrequency of a system constrains the performance of its corresponding QHT, and QHTis considered insufficient to describe the complexity of VAWT systems.UBEM is an analytical model based on potential flow theory, which reduces thedimension of the problem by refining the problem to the hydrofoil boundary instead ofthe entire flow domain. It solves the Laplace equation for the velocity potential basedon the kinematic boundary conditions along the hydrofoil surface and the pressureKutta condition at the trailing edge. By modeling the continuous dipole/vortex wakesheet behind the trailing edge, UBEM accounts for the wake effect. This study avoidsthe singularity caused by foil-wake intersection by retaining the latest generated wakesheet to allow continuous revolutions. The results of UBEM have shown that it caniiieffectively predict the hydrofoil pressure distribution and torque performance resultsfrom RANS, with significantly less computation time. Additionally, the wake sheetgenerated by UBEM aligns well with the wake development seen in RANS vorticitycontours. This study also highlights the challenges of the current UBEM, including thedifference from RANS during the early ramp stage and the limitations in the adoptedsingularity-avoiding strategy in foil-wake intersection.