A crucial aspect in the numerical simulation of mechanical phenomena is the representation of arbitrary domains, especially when they evolve in time. Eulerian formulations, specifically the ones that implicitly define the geometry by using level-sets (LS), have been largely employed in applications concerning numerical simulation of free surface moving fluids and numerical simulation of multiphase fluid flows. Such interest in LS techniques is due to the fact that these methods are able to efficiently handle topological changes of the free surface and are easy to code. On the other hand, numerical errors in the transport of the LS function causes significant collateral effects, not just on code accuracy, but also on its robustness and stability. Spurious loss or gain of mass, momentum and energy may in fact completely invalidate the numerical simulation. In this project, we propose the use of Lagrangian marker particles and local/global minimization techniques for the correction of LS functions. A clever use of the Lagrangian information will lead to improved accuracy and better mass preservation, keeping however the geometrical and topological flexibility of LS methods. In addition, a derived research theme is being proposed in order to define novel semi-Lagrangian schemes for free surface flow by means of meshless interpolation/approximation approaches from unorganized points, which can be based on moving least-squares, radial basis function or partition of unity. This last application has received much attention in Approximation Theory with several applications in Computer Graphics.
News published in Agência FAPESP Newsletter about the scholarship: