| Author | Message | ||
     Mohammad Rahmani (mohammad) New member Username: mohammad Post Number: 1 Registered: 12-2003 |
How can we difine PDEs governing on different domains? I am working on modeling catalytic reaction which means a tube containing alot of spherical or cylindrical pellets. Normally we use two different geometries and coordinates for such a problem, in each domain one PDE is governing while it is not valid on the other domain. So, I have two domains, the first is tube, a rectangular domain with specified PDE and BCs. The other domain is a sphere here modeled as a circle with another PDE and BCs. I want to define the equations and domains in such a way in each domain its PDE can be solved. These two domain will be coupled through a variable at their boundary. Is it possible to define such a domains and equations? Merry Christmas and Happy new year Thanks in advance Mohammad | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 80 Registered: 06-2003 |
FlexPDE treats partial differential equation systems in two or three dimensions. It is nowhere required that these two or three dimensions actually correspond to physical dimensions of "real" space. As long as you can state a well-posed system of PDE's in two or three dimensions, and map these dimensions to a domain which can be plotted on the graphic screen, the requirements of FlexPDE are met. One technique which has been used in problems like yours is to define the X dimension as distance along the tube, and the Y dimension as radial coordinate inside a typical sphere located at that X position along the tube. You can provide X-derivative terms to represent x_diffusion or flow down the tube, and spherical diffusion terms in Y to represent diffusion into the spheres. Define two variables, one for the substance in the tube, the other for the substance in the spheres, and couple them at the top boundary of the rectangular logical domain in X-Y. FlexPDE requires that all variables be defined everywhere in the domain, so your tube-propagation variable is meaninglessly replicated throughout the Y-dimension. So what, computers are cheap. Give the tube variable a large diffusion in the Y dimension, and a reflective BC on the bottom, so you get uniform concentration throughout Y. For graphical display reasons, you should probably scale the Y-dimension to give a pleasing plot. |