Solving Diffusion Equation By Finite difference Method in fortranby cool2shiv Tags: diffusion, finite difference, fortran, fortran 77, pde 

#1
Mar2011, 05:16 PM

P: 5

Hey,
I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper surface of drop as well as the leaf and dc/dz = 0 for the bottom most layer and the width is taken very large Can anyone help me please in making the grid for using FDM the Droplet is not hemispherical in shape. 



#2
Mar2211, 03:26 AM

P: 605

What is dc/dn? From your equation you have three independent variables: z, r, and t.
Edit: Oh silly me I get it sorry. 



#3
Mar2211, 08:09 AM

P: 5

the flux perpendicular to the surface of the drop is zero.
So, have you any idea what should i do? 



#4
Mar2811, 08:52 AM

P: 81

Solving Diffusion Equation By Finite difference Method in fortran
you can generate the meshes as all rectangles of different sizes, in matlab, FORTRAN, c++, etc. Just set up a 3D matrix to account for changes in time, r,z. You can then discretize the equation via finite difference from that to go from there. Talk to me if you need additional help.




#5
Mar2811, 05:07 PM

P: 5

Hey thanks a lot... but how will i use the boundary condition on the curved surface i.e dc/dn=0
i.e flux perpendicular to droplet is 0. for that i think i will need the points on the surface of the droplet (not hemisphere) and the point which is on the line perpendicular to the surface of the droplet... please tell me how to make grid... and how to use the boundary condition dc/dn=0 i will be thankful to u for this. 



#6
Mar2811, 06:53 PM

P: 81

Ok? 



#7
Mar2911, 12:40 AM

P: 5

yeah that is fine..but How will i find the points on the hemisphere???
i mean how will i make sure that the corners of the rectangles fall on the hemisphere?? as i can only fond the values at the corners of a rectangle? Did u get what i am trying to ask? 


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