Project 1: two-dimensional, standard, linear wave equation, with damping

Overview

This project is a finite difference implementation in python/ numpy. It is used to compute two dimensional waves. The behavior of waves as they pass through different mediums with different velocities are studied and reported, see report_wave_project.pdf. The implementation of the numerical solution can be found in wave2D.py. There is a function for every task that computes and animates the result. If you want to know how the animation works, see test_animation.py.

The following sections demonstrate some examples.

Verification: Exact 1D plug-wave solution in 2D

There is a pulse function that is split into two identical 1D waves. They are moving in opposite direction, exactly one cell per time step. The discrete solution is then equal to the exact solution.

Pulse in x-direction	Pulse in y-direction

Verification: Standing, undamped waves

Exact solution as a colored surface, numerical solution visualized as a grid.

Verification: Standing, damped waves (manufactured solution)

Exact solution as a colored surface, numerical solution visualized as a grid.

Investigation of a physical problem: Tsunami over a subsea mountain