**Keywords:**Surfaces | Catmull-Clark subdivision | Differential operators | GPU | cuda | efficiency | Fluid simulation | Reaction- Diffusion

In recent years, many researchers have used the Navier-Stokes equations and Reaction-Diffusion systems for fluid simulation and for the creation of textures on surfaces, respectively. For this purpose it is necessary to obtain information about operators de- fined on surfaces. We obtained the metric information of the dis- tortion caused by the parametrization of Catmull-Clark subdivi- sion surfaces. Then the Navier-Stokes equations and the systems of Reaction-Diffusion on surfaces are solved in the domain of parametrization of each surface patch. The solution can be com- putationally expensive, but this process can be done in parallel for each point in the discretization of the surface, so a GPU implemen- tation can heavily speed up the computation.