A time accurate high order numerical simulation on parallel computers is used to study traveling wave streaming and its suppression using a jet pump. A unidirectional finite amplitude traveling wave is generated using two line sources located a quarter wavelength apart and π/2 out of phase. First, a channel with a uniform cross section is considered and the code is validated for three different cases for which analytical solutions are available. Then numerical simulations are performed for two different geometries, an orifice and a jet pump, and their results are compared. It is shown that a net mean pressure difference is developed across the jet pump that is due to asymmetry in the minor losses. This pressure difference could be used to suppress traveling wave streaming. The mean temperature, density, and Eulerian velocity are also calculated and compared for both the jet pump and orifice.