lynx-delta / hyper_pde_1d_travelwave

Hyperbolic partial differential equation solver: visualization of 1-dimensional travelling wave (for teaching purposes)

hyper_pde_1d_travelwave

Hyperbolic partial differential equation solver: visualization of 1-dimensional travelling wave (for teaching purposes)

Wave Equation with Non-constant Wavespeed

The scripts in this repository are used to solve and visualize the hyperbolic Partial Differential Equation (PDE) governing the motion of a tsunami (or similar) in the open ocean, in the case of a variable height seabed:

with u(x, t) the non-dimensional sea surface height and h(x) the non-dimensional still-water height (see figure below).

The initiation of the tsunami (e.g. a subsea earthquake) can be modelled by the initial displacement

centered at x₁, with (additional) sea surface height α₁ and spread σ₁. The subsea hill (or depression) is modelled as

with the center at x_B, the elevation α_B and the spread σ_B. To model infinite spatial domains, an open boundary at x = 0 respectively at x = L given by the condition

is implemented.

Solution and Visualization

The hyperbolic PDE is solved employing finite difference methods. To model, solve and visualize the hyperbolic PDE for time t, use the files pde_hyper_1Dtravelwave.py and pde_DEMO_1Dtravelwave.py.

For an animated solution, use file pde_hyper_1Dtravelwave_anim.py (pde_hyper_1Dtravelwave.py is imported and used for solving the PDE for a certain time frame).