The study focuses on investigating the phenomenon of wave scattering caused by an impermeable circular cylinder partially immersed in water using the well-known eigenfunction matching method. The study employs the pertaining boundary conditions to deduce the unknown potentials in both the exterior and interior regions. The Bessel and Hankel functions are utilized to express the velocity potential in each region. The extended expressions of the velocity potentials involve unknown coefficients that are found using the well-known eigenfunction expansion approach. The code is validated with the available results in the literature. To study the evolution of the solution in time, time-marching simulations of the fluid flow are presented, which provide a different approach to visualizing wave scattering by the structure.