Phase-field modelling of evolving interfaces

Project description

Phase-field modelling of evolving interfaces (Or – How does one effectively model and simulate interfacial phenomena?)

Evolving interfaces are ubiquitous in nature, think of the melting of the polar ice caps, the separation of oil and water, or the growth of cancerous tumours. Two mathematical descriptions exist to model evolving interfaces: those with sharp-interface descriptions, such as parametric and level-set methods, and those with diffuse-interface descriptions, commonly referred to as phase-field models.

Challenges for students:

• Can one develop a phase-field model for a particular interfacial phenomenon?
• What are the foundational laws underpinning phase-field models?
• What is the connection between sharp-interface models and phase-field models?
• Can one design stable time-stepping schemes for phase-field models?
• Or efficient adaptive spatial discretisation methods?

Depending on the interest of the student, one of these issues (or others) can be addressed. Also, the student is encouraged to suggest a second supervisor, possibly from another group!