developed to facilitate the use of the level-set method in computer applications. Applications Computational fluid dynamics Combustion Trajectory planning Optimization Image processing Computational biophysics Discrete complex dynamics: visulalisation of parameter plane and dynamic plane Computational fluid dynamics To run a Math Model in the interface of two different fluids we need to soften the interactions between the fluids. Therefore we need to apply a specific function: Compact Level Set Method. As a “spin off”, the CompactLSM is a complement of the LSM, that helps solving LSM equations. It can be used in numerical simulation of flow, for example, if we are working with discretization of the interface water-air, compacts at sixth order, ensures the accurate and fast calculation of the interface equations (Monteiro 2018). The LSM uses a distance function to locate different fluids. A distance function is that whose value represents the smallest distance from the point where it is being analyzed to the interface. This distance function is identified by isolines (2D) or isosurfaces (3D), showing that the negative values refer to one of the fluids, positive values refer to the other and the zero value corresponds to the position of the interface. But, how is the Heaviside function inserted in the Compact Level Set Method? Since the specific mass and viscosity are discontinuous at the interface, both excess diffusion problem (interface widening) and numerical oscillations are expected if there is no adequate treatment of the fluid near the interface. To minimize these problems, the Level Set method uses a smooth, cell-related Heaviside function that explicitly defines the interface position (∅ = 0). The transition in the interface is kept smooth, but with a thickness of the order of magnitude of the cell size, to avoid the introduction of disturbances with a length scale equal to that of the mesh, since the interface infers an abrupt jump property from one cell to the next (Unverdi and Tryggvason, 1992). To reconstruct the material properties of the flow, such as specific mass and viscosity, another marker function, I (∅), of the Heaviside type is used: where δ is an empirical coefficient, usually equal to 1; 5 and Δ is the characteristic discretization of the problem, which varies according to the phenomenon to be simulated. The value of δ represents an interface with a thickness of three cells, and thus δΔ represents half the thickness of the interface. Note that in