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2D diffusion equation using Finite volume method

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Old   March 21, 2020, 02:17
Lightbulb 2D diffusion equation using Finite volume method
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Mudit Mehta
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Hey, i am working on an assignment problem:
Consider a two-dimensional rectangular plate of dimension L = 1 m in the x direction and H = 2 m in the y direction. The plate material has constant thermal conductivity. The steady-state temperature distribution within this plate is to be determined for the following imposed boundary conditions: (i) y = 0, T = 100 ̊C, (ii) x = 0, T = 0 ̊C, (iii) y = H, T = 0 ̊C, and (iv) x = L, T = 0 ̊C. Choose a uniform grid size of 0.05 m in both directions. Solve the problem using the point-by-point Gauss-Seidel iterative method. Experiment with the
initial guess and comment on the number of iterations required for convergence in each case. Clearly explain your convergence criterion for the iterations and how it is implemented. Plot the temperature contours as the output.

I have solved this question in python and i am getting following results:
When initial guess = 0, No of iterations = 350
Now when i am taking initial guess less than 10 i get less no. of iterations but when i take initial guess to be larger than 10 i get larger number of iterations.
Can anyone explain. Please it is very urgent and important.
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2d diffusion equation, finite volume method, python

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