When Euler meets Lagrange: Particle-Mesh Modeling of Advection Dominated Flows

This thesis presents a numerical framework for simulating advection-dominated flows which reconciles the advantages of Eulerian mesh-based schemes with those of a Lagrangian particle-based discretization strategy. Particularly, the strategy proposed in this thesis inherits the diffusion-free properties as in Lagrangian particle-based advection,...

Development of a fully discontinuous Hybrid Spectral Finite Element Method: Solution of the vector Laplace and the Stokes’ equation

Being able to solve numerically partial differential equations is fundamental for engineers to evaluate, optimize and improve industrial equipments. The framework of mimetic finite element methods allows engineers to find solutions characterized by strong conservation properties: this may result in a pointwise divergence free-flow field. However...

Energy Stable and Momentum Conserving Hybrid Finite Element Method for the Incompressible Navier–Stokes Equations

A hybrid method for the incompressible Navier–Stokes equations is presented. The ethod inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods hen momentum advection becomes significant, equal-order interpolations can be used for the velocity nd pressure fields, and mass can be conserved locally. Using continuous...