Fluid simulation is an essential tool to produce realistic looking animations. In particular, Lagrangian simulations offer interactive computation times with an easy integration of the two-way interaction with rigid bodies. However, the interactivity is lost for larger scenes even if only the areas around the bodies have any visual interest. In this paper, we present a novel approach to quickly initialize additional fluid in a rest state in simulations with any 3D boundary shape and able to preserve any already existing fluid. Our approach only uses the density property of the particles to allow compatibility with any smoothed-particle hydrodynamics (SPH) simulation scheme and any boundaries model. This initialization method is fast enough to allow the initialization of new fluid volumes interactively while the simulation is running. We showcase our approach by proposing a method to create a dynamic simulation window, allowing the restriction of simulating the fluid only around moving objects. We propose multiple experiments to demonstrate the capabilities and performance of our approach.