|May 17, 2016, 07:16||
Finite Difference for Laplace Operators
Join Date: Feb 2016
Posts: 13Rep Power: 2
I am working on the finite volume method on a clustered Cartesian grid for school. I am using a finite difference function I made previously to get the operators for u,v,d u/v d x/y for solving the Poisson equation.
The function evaluates the taylor expansion for each point of stencil x of phi about x0 and returns the coefficient matrix
[phi^1] = A* [phi_i ]
I am looking for the zeroth derivative of the phi as I am trying to use this to interpolate the value itself. How do I go about this? I have the values of phi on other points, but not on x0 itself.
Any help would be great
|May 17, 2016, 11:06||
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,695Rep Power: 33
the zeroth derivative of phi in x0 is phi(i) ...
f(i+1) -f(i) = h* df/dx|i + h^2/2*d2f/dx^2|i + ...
f(i+1)-f(i) = -h* df/dx|i + h^2/2*d2f/dx^2|i
deltaf = A * derivatives + hot ->
derivatives = A^-1*deltaf - A^-1*hot
A is 2x2. Then, you disregard A^-1*hot and you get the vector derivatives_n which approximates the exact derivative
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