PhD defense - Alejandro QUIRÓS RODRÍGUEZ

Abstract:
"Numerical methods for modeling and optimization of interfacial flows"
In the first part of this thesis, a novel conservative cut-cell method is developed to simulate interfacial flows. This cut-cell method is coupled with the level-set method to capture the interface motion. Special care is taken so that the discrete operators mimic their continuous counterparts, so that both primary and secondary quantities such as the kinetic energy are conserved in the applicable limits. The methodology is first applied to stationary interfaces. Poisson's equation is employed for validation and in order to showcase the ease with which mixed boundary conditions are implemented. Various canonical flows are then considered, including the flow around a cylinder and the flow around an airfoil. Next, the methodology is extended to moving interfaces, in the context of free-surface flows and contact line dynamics. The spreading of a two-dimensional droplet is used as test case. The spreading over a straight surface is first considered, prior to the spreading over arbitrarily shaped surfaces, which requires the extension of the cut-cell formalism to a second level-set function to capture the solid boundary.
In the second part of the thesis, optimization algorithms that do not require the computation of an exact gradient, as exemplified by the adjoint-state method, are evaluated. Such alternatives are particularly suitable for interfacial flows due to the complexity of developing an adjoint solver in such cases. In particular, the performance of the surrogate model based optimization algorithm DYCORS and the performance of the EnVar method are assessed. The former one is applied to the optimization of high fidelity simulations, whereas the latter one is employed to perform nonlinear stability analysis, by reformulating the stability analysis as an optimization problem. The non-modal stability analysis of a cavity flow and the Floquet stability analysis of the flow around a cylinder are used to assess the performance of the algorithm. Finally, the optimization of a free-surface flow with contact line dynamics is presented.