Numerical Method for a Free-Boundary Problem

In 3D printing of metals, thin and precise lines must be produced. Due to the high surface tension of liquid metals, free boundaries in metal printing are governed by capillary forces, and inadequate experimental conditions may lead to undesired ripples on printed structures due to capillary waves. As a result, high-fidelity simulations are required in order to capture the subtle dynamics of menisci and establish appropriate printing conditions.
In this semester project, a student would be tasked with implementing a numerical method (preferably finite elements) for the nonlinear ODE governing the free boundary of a flowing liquid metal in the steady-state, governed by surface tension. Upon validation, the method could be integrated into an existing code for the simulation of a full, free-boundary PDE, relevant to the research of 3D printing of metals. Finally, if time permits, the student could either explore convergence of their method from a theoretical perspective, study stability of their predicted equilibrium point using the calculus of variations, or introduce Marangoni effects (varying surface tension) into the model. The choice of the second part may vary depending on the status of LMM’s current research project.

Responsible supervisor: Tyler Benkley

Contact: [email protected]