Métodos particle-in-cell para simulação anisotrópica de fluidos

Abstract

This work presents two method to redirect a fluid flow using tensor fields in particlein-cell based simulations. Our focus is use tensor fields as medium to deflect fluids for computer graphics effects. This work adapts the classical formulation of the Fluid-ImplicitParticle (FLIP) method including the information of the tensors during the projection and advection steps. Two new numerical approaches for solving anisotropic projection will be presented, one based on faces and other based on faces and edges. The development of these methods aims to ensure a stable, smooth and divergence-free simulations. For this purpose, two staggered grid structures are employed. The classic Marker-and-Cell (MAC) grid is used to store the velocity field and to find the field projected by the face-based projection. However, to accommodate values stored on edges, an extension to this grid category is proposed, which is used in face and edge based projection. A new third order Runge-Kutta method is proposed, where we incorporate the tensor deflection as an acceleration field. An external force is also proposed to balance the tensor effects on the fluid-empty boundary. Such a force acts to evolve the flow in the region, causing the tensor field to exert an effect on a permeable medium. To show the capabilities of each approach, individual tests will be executed with different categories of tensor fields. In addition, a comparative experiment is presented to analyse the visual and numerical aspects of each method. With the experiments it is possible to understand how the different types of tensors affect the fluid with different approaches.