Abstract
The equation modelling the evolution of a foam (a complex porous medium consisting of a set of gas bubbles surrounded by liquid films) is solved numerically. This model is described by the reaction-diffusion differential equation with a free boundary. Two numerical methods, namely the fixed-point and the averaging in time and forward differences in space (the Crank-Nicolson scheme), both in combination with Newtons method, are proposed for solving the governing equations. The solution of Burgers equation is considered as a special case. We present the Crank-Nicolson scheme combined with Newtons method for the reaction-diffusion differential equation appearing in a foam breaking phenomenon.
| Original language | English |
|---|---|
| Pages (from-to) | 317-330 |
| Number of pages | 14 |
| Journal | ANZIAM Journal |
| Volume | 51 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jan 2010 |
| Externally published | Yes |
Keywords
- breaking front
- Crank-Nicolson method
- foam drainage
- free boundary problem
- nonlinear partial differential equation
- Plateau border
- reaction-diffusion problem