Fluids are extremely common in our world and play a central role in many natural phenomena. Understanding their behavior is of great importance to a broad range of applications and several areas of research, from blood flow analysis to oil transportation, from the exploitation of river flows to the prediction of tidal waves, storms and hurricanes. When simulating fluids, the so-called Eulerian approach can generate quite correct and precise results, but the computations involved can become excessively expensive when curved boundaries and obstacles with complex shapes need to be taken into account. This work addresses this problem and presents a fast and straightforward Eulerian technique to simulate fluid flows in three-dimensional parameterized structured grids. The method s primary design goal is the correct and efficient handling of fluid interactions with curved boundary walls and internal obstacles. This is accomplished by the use of per-cell Jacobian matrices to relate field derivatives in the world and parameter spaces, which allows the Navier-Stokes equations to be solved directly in the latter, where the domain discretization becomes a simple uniform grid. The work builds on a regular-grid-based simulator and describes how to apply Jacobian matrices to each step, including the solution of Poisson equations and the related sparse linear systems using both Jacobi iterations and a Biconjugate Gradient Stabilized solver. The technique is implemented efficiently in the CUDA programming language and strives to take full advantage of the massively parallel architecture of today s graphics cards.