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Real-time haptic rendering of three-dimensional fluid flow will improve the interactivity and realism of applications ranging from video games to surgical simulators, but it remains a challenging undertaking due to its high computational cost. Humans are very familiar with the look and feel of real fluids, so successful interactive simulations need to obey the mathematical relationships of fluid dynamics with high spatial resolution and fast temporal response. In this work we propose an innovative GPU-based approach that enables real-time haptic rendering of high-resolution 3D Navier-Stokes fluids. We show that moving the vast majority of the computation to the GPU allows for the simulation of touchable fluids at resolutions and frame rates that are significantly higher than any other recent real-time methods without a need for pre-computations. Based on our proposed approach, we build a haptic and graphic rendering system that allows users to interact with 3D virtual smoke in real time through the Novint Falcon, a commercial haptic interface.