A computer implemented method for simulating a final pattern of a droplet of a fluid having a plurality of fluid properties is disclosed. The method includes representing a position of a moving fluid boundary at a first point in time with a plurality of fluid markers, wherein the moving fluid boundary provides a boundary for a single-phase fluid. The moving fluid boundary separates a simulation space into a fluid space and a vacuum space, and the single-phase fluid inhabits the fluid space. The method further includes evaluating a plurality of indicator function defined on a quadrilateral grid for a velocity field, a pressure, and the plurality of fluid markers. The quadrilateral grid is formed by a plurality of points inside the fluid space and the vacuum space. The method also includes calculating surface tension at the moving fluid boundary through a level set method, solving a plurality of flow equations through a projection method for a surface location on the boundary, and representing the position of the moving fluid boundary at a second point in time by updating the positions of the fluid markers based on the plurality of velocity values. The fluid properties and the shape of the final pattern is then stored on a computer readable media.