Solving Diffusion Equation By Finite difference Method in fortran

cool2shiv

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.

Attached Thumbnails

 

Winzer

What is dc/dn? From your equation you have three independent variables: z, r, and t.

Edit: Oh silly me I get it sorry.

cool2shiv

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

yus310

you can generate the meshes as all rectangles of different sizes, in matlab, FORTRAN, c++, etc. Just set up a 3-D 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.

cool2shiv

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.

yus310

model everything as a bunch of rectangles.. hemisphere is small rectangle on top of the other two rectanges.. simply the bc, dc/dn=0 at the hemisphere/rectangle or that C(i+1,j)-C(i,j)/(delta(x)=0, so C(i+1,j)=C(i,j) at the hemisphere barrier.... meshes can be made by filling up matrices with zeroes and making these matrices based on size of rectangle e.g. 5 m X 5 m rectangle can be a 5 X 5 matrix, if the units are "m".. get my drift? do the same with the other rectangles, keeping respect to orientation and size and keep everything in one mesh?

Ok?

cool2shiv

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?