PDE in time varying domain

Hello all!

Is it in some way possible to specify a 2D PDE to be solved on a time varying domain? Something like this:

instant t=0: 2D pde on domain(t=0)

instant t=1: 2D pde on domain(t=1)

and so on. The evolution of the domain is known.

thank you!

Answer 1

[Deepak Ramaswamy]

Patric,

It would be helpful to get details on the PDE formulation that shows how the domain evolves. I assume domain refers to geometry otherwise my comments that follow are not relevant. PDE Toolbox (for 2-D spatial problems) works directly with fixed geometry. Evolving geometries can sometimes be mapped to this fixed geometry via a transformation. Example: Lagrangian formulation for geometrically nonlinear problems. The general idea is to change the PDE (constitutive equations, Boundary conditions) such that the geometry is fixed.

Best, Deepak