# Heat conduction with spatially varying conductivity

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 March 22, 2016, 21:48 Heat conduction with spatially varying conductivity #1 New Member   Terry Tensinsky Join Date: Feb 2010 Posts: 14 Rep Power: 15 Hello everyone, I am trying to solve a problem like \nabla(D\nabla T) +f =0 where D is a function of x and y, (x,y being the coordinate system) with some well defined boundary conditions (Dirichlet or Neuman). I want to have a simple FDM discretization like Gauss Seidel or SOR method, but since D is varying spatially I doubt that my simple scheme can work. Does anyone know any better solution? Thanks,

March 23, 2016, 03:43
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,599
Rep Power: 70
Quote:
 Originally Posted by hami9293 Hello everyone, I am trying to solve a problem like \nabla(D\nabla T) +f =0 where D is a function of x and y, (x,y being the coordinate system) with some well defined boundary conditions (Dirichlet or Neuman). I want to have a simple FDM discretization like Gauss Seidel or SOR method, but since D is varying spatially I doubt that my simple scheme can work. Does anyone know any better solution? Thanks,

I do not understand your question... GS, SOR are iterative algorithms for solving algebric linear systems, are not FDM discretization...

In second order discretization you can proceed for example:

[(D* dT/dx)|i+1/2-(D* dT/dx)|i-1/2]/dx

 Tags conduction, fdm, sor