elastic-membrane-2D

Overall this repo aims to model 2D droplet impact onto an elastic membrane. The position of the elastic membrane at $z = -w(x, t)$ is given by the PDE

$\alpha w_{tt} - \beta w_{xx }+ \gamma w_{xxxx} = p(x, t)$,

where $p(x, t)$ is the pressure along the membrane. The repo is split in these directories:

finite_differences: Code to solve the membrane equation using finite difference methods. This contains code (in C or MATLAB) for the algorithms, but for a given pressure function $p(x, t)$ in order to develop and verify the methods normal_modes: Code to solve the membrane equation using the normal modes method, usually purely in MATLAB. This has the algorithms for given pressure functions, but not fully coupled droplet_impact: Code to solve the coupled problem where the pressure $p(x, t)$ is taken from the pressure in the droplet responding to the motion of the membrane. This is either an analytical model taken from Wagner theory, or a numerical model using VOF simulations.