Tutorial 3: Sponge Boundary Conditions

This tutorial describes how to add sponge boundary conditions. By default, Jaxion uses periodic boundary conditions. Sponge boundary conditions can be used to absorb outgoing waves at the domain boundaries.

An example of sponge boundary conditions is provided in examples/tidal_stripping

It is created by adding an imaginary external potential to the simulation. We need to set params["physics"]["external_potential"] = True, and define sim.state["V_ext"] on the grid:

# V_0 is the depth of the sponge potential ~ G * M_tot / box_size
# r_N, r_p, and r_s define the sponge region
r_N = 0.5 * box_size
r_p = (7 / 8) * r_N
r_s = 0.5 * (r_N + r_p)
delta = r_N - r_p
V_sponge = (
    -0.5j
    * V_0
    * (2 + jnp.tanh((R - r_s) / delta) - jnp.tanh(r_s / delta))
    * jnp.heaviside(R - r_p, 0.0)
)
sim.state["V_ext"] = V_sponge

Since the sponge potential is imaginary, it will absorb outgoing waves in the sponge region.