Homogeneous Dirichlet

Homogeneous Dirichlet conditions force the wavefield to be zero at the specified boundary.

In the scalar acoustic case, this simply gives

\phi = 0,\quad\text{on~}\Gamma,

and in elastic media, we obtain

u = 0,\quad\text{on~}\Gamma.

It is possible to fix only certain components of the displacement field $u$ in the elastic case.

Practical Advice

For coupled simulations of waves propagating along a fluid-solid interface, the homogeneous Dirichlet condition is the physically correct condition to describe the “free-surface condition” in water.