Thank you and the sibling comment. These are interesting resources for practical and physical simulations of real phenomena.

I thought more about an idealized wave (which water waves are not) through a homogeneous euclidean medium of idealized single oscillators. Each oscillator can only communicate to its direct neighbors.

I should read through some of your materials as this might be what they talk about in the first chapters. But they focus too much on the actual physics and less about the implementation.