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In other words, Always do mesh refinements until the solution converges. If you don't, it is possible your simulation may be completely off from reality, and will be useless!
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https://confluence.cornell.edu/download/attachments/146918522/Convergence.png
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Compare this to the analytic solution, and note how it converges on the same line:
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Note that Theta, x, and y defined as dimensionless temperature, x coordinate, and y coordinate respectively. The X and Y were reduced by the width W.newwindow