We present a novel method for simulating liquid with asynchronous time steps on Eulerian grids. Previous approaches focus on Smoothed Particle Hydrodynamics (SPH), Material Point Method (MPM) or tetrahedral Finite Element Method (FEM) but the method for simulating liquid purely on Eulerian grids have not yet been investigated. We address several challenges specifically arising from the Eulerian asynchronous time integrator such as regional pressure solve, asynchronous advection, interpolation, regional volume preservation, and dedicated segregation of the simulation domain according to the liquid velocity. We demonstrate our method on top of staggered grids combined with the level set method and the semi‐Lagrangian scheme. We run several examples and show that our method considerably outperforms the global adaptive time step method with respect to the computational runtime on scenes where a large variance of velocity is present.