Fast barotropic gravity waves in the ocean require that an efficient computational method is applied in ocean models used for climate simulations. The Gravity Wave Retardation (GWR) method is a simple technique that slows down surface waves and allows a simple explicit integration to be used. Here the method is discussed and applied to a layer model of the tropical Indian Ocean subject to monthly climatological wind forcing. The errors introduced by the GWR method on the barotropic ocean circulation and sea surface elevation are analysed. Comparison to a model integration with a flat bottom demonstrates that GWR integrations with speed-up factor up to 16 indeed capture some influence of the bottom relief, in the sense that the GWR solutions have less error than if topography was ignored. Integrations with a speed-up factor of up to 8 are found to model the barotropic circulation well, implying that the GWR method can be applied to climate modeling.