Thursday, December 1, 3:00PM
NSH 1507
Benoit Hudson
How to mesh when the ground is moving
Traditionally, finite element simulations have assumed the geometry of the domain is fixed — after all, in a weather simulation, the mountains do not move. However, in many problems the geometry does, in fact, change — very notably so in solid deformation problems (bending a steel bar, for instance) and in fluid-solid interaction problems (blood cells flowing through a capillary). Even when the geometry is fixed, it can be helpful to write the equations in a Lagrangian frame of reference, which requires that we allow mesh elements to move and deform over time. I will survey various methods to deal with moving boundaries and moving mesh elements. As a geometer, I will naturally bias towards techniques that leave the mathematics quite simple at the cost of making the geometry difficult. We will see that while the state of the art has progressed to the point of making pretty pictures, the field is still wide open.
