A fixed domain method for diffusion with a moving boundary

✍ Scribed by L. W. Morland

• Publisher: Springer
• Year: 1982
• Tongue: English
• Weight: 488 KB
• Volume: 16
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00042720

✦ Synopsis

The one-dimensional diffusion equation for a region with one fixed boundary and one unknown moving boundary is transformed to a non-linear equation on a fixed region by using the moving boundary position as the time variable. The boundary velocity becomes a second dependent variable, with dependence only on the new time variable. An implicit finite difference scheme, marching in time, is applied to a problem with known analytic solution to demonstrate the computing speed and accuracy of this approach, and also to a problem solved previously by variable time step methods. This transformat!on reduces any parabolic or elliptic system of equations on a domain with moving boundary, or with unknown free surface in two space variables, to a non-linear freed domain system which has advantages for computation.