An electronic apparatus performs a method of real time simulation of physical visual effect on one or more Graphics Processing Units (GPUs). The method includes a plurality of time steps. Each of the time steps includes: building up a mapping between particles and background grid blocks; sorting the particles to a level of granularity; transferring momenta and masses of the particles to grid nodes on the background grid blocks to compute forces on the grid nodes; updating velocities and resolving collisions from the computed forces on the grid nodes; and applying the updated velocities back to the particles from the grid nodes and advecting the particles. In some embodiments, the frequency of building up and sorting is reduced compared with the frequency of transferring, updating, and applying in the plurality of time steps.