We consider a wave energy device consisting of a thin vertical surface-piercing barrier next to a vertical wall in finite depth water. Power is extracted due to a normally incident wave forcing the free surface of the fluid between the barrier and the wall to oscillate, in turn pumping the volume of air above the free surface through a uni-directional turbine housed at the opening of the device. Under the assumptions of linear water wave theory, the important hydrodynamic properties are expressible in terms of integral quantities of functions proportional to the fluid velocity under the barrier. These functions each satisfy integral equations, the solutions of which are approximated very accurately and efficiently using a Galerkin method as described in Porter and Evans [Porter, R. & Evans, D. V., Complementary approximations to wave scattering by vertical barriers. J. Fluid Mech., 294 (1995) 155–80].