Master's Thesis Final Project:
Catmull-Clark Subdivision Surfaces
Implemented the original algorithm by Catmull-Clark for closed surfaces. The phrase subdivision surfaces, in the field of 3D Computer Graphics, refers to a class of surfaces that are obtained with the aid of computers through repeated refinements of their control points polyhedra. The Catmull-Clark subdivision algorithm works on polyhedra with arbitrary topology, and the limit-surface generated is a uniform bicubic B-spline surface of class C2, except at points that have a number of adjacent edges different from four, called extraordinary points, where they have C1 continuity.
Expanded the original algorithm, that only accounted for closed surfaces, to include open surfaces. In this case, the boundary conditions were considered following the approach by Nasri (i.e. the auxiliary ghost nodes were found by linear extrapolations of the internal nodes).
Numerical Simulations of Thin Viscoelastic Films
Carried out a computational investigation, in the field of Computational Fluid Dynamics, for thin viscoelastic films on a flat solid substrate subject to the van der Waals interaction force. The governing equations are obtained within a thin film approximation of the Navier-Stokes equations with Jeffreys model for viscoelastic stresses. The resulting equation is a second order in time and fourth order in space Partial Differential Equation. The numerical method chosen is an implicit finite difference scheme, with adaptive time step discretization and fixed grid size. The investigation focused on the effects of non-Newtonian viscoelasticity, Newtonian viscosity, and the substrate slippage on the dynamics of thin viscoelastic films. This work is part of my PhD thesis project, developed within the Complex Flows and Soft Matter Group, and it has been published in V. Barra, S. Afkhami, L. Kondic, Interfacial dynamics of thin viscoelastic films and drops, Journal of Non-Newtonian Fluid Mechanics, 237, (2016), 26-38
Numerical simulations of a spreading non-Newtonian viscoelastic drop (red solid) compared to a Newtonian one (blue dotted) on a flat solid substrate. We found that elastic effects lead to deviations from the Cox-Voinov law for partially wetting fluids. In general, elastic effects enhance spreading, and suppress retraction, compared to Newtonian ones. This work is part of my PhD thesis project, developed within the Complex Flows and Soft Matter Group, and it has been published in V. Barra, S. Afkhami, L. Kondic, Interfacial dynamics of thin viscoelastic films and drops, Journal of Non-Newtonian Fluid Mechanics, 237, (2016), 26-38
Pixar Animation Studios Internship Project:
Numerical Simulations of Viscous Liquids on Surfacess
Interned in the Research group at Pixar Animation Studios. Developed a proprietary C++ library for a 2D Navier-Stokes solver for viscous fluid simulations on surfaces with arbitrary curvature. Expanded existing code to include different types of discretized domains (from triangular to polygonal meshes). Included user-defined solid obstacle and boundary conditions for open meshes. Prototyped the development of a plug-in for third-party procedural 3D animation and special effects software for film and entertainment, Houdini by SideFX. Developed a proprietary C++ library to simulate the dynamics and interface instabilities of 3D thin viscous films on triangular surfaces with arbitrary curvature.