For many fluid dynamics simulations, low viscosities allow for the usage of fast fractional step schemes. Computing the velocity explicitely allows for an important reduction in the computational time required per time step. However, one of the main limitations of Eulerian explicit fractional step solvers is the presence of the non-linear convective term. This factor reduces the maximum possible time step, increasing the number of steps needed and therefore the total time required for the simulation. Also the linearization of the equations translates into poor solutions.

In the RealTime project, a new strategy was developed to tackle this problem. By using a Lagrangian formulation, the convective term vanishes, therefore allowing for an explicit treatment of the pressure without the limitations of Eulerian counterparts. Moreover, integrating the forces along the streamlines of the material points that define the continuum, it was possible to provide a better aproximation to the non-linear convective movement in a single, explicit step. This allowed for a fast solver that is accurate even for very large time steps, requiring only the pressure to be calculated implicitely. The result of this work lead to the creation of the Particle Finite Element Method , second generation (PFEM2). Two implementations were developed, fixed mesh strategy (using projection) and a moving mesh strategy (using remeshing). Below several examples can be seen.