l10 - Lecture 10: A First Look at the Diffusion Equation...

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1 Lecture 10: A First Look at the Diffusion Equation - Unsteady Conduction
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2 Last Time… Looked at Under-relaxation » Gives user control over the iteration process in non- linear problems » Can be used to promote diagonal dominance Line-by-line TDMA
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3 This Time… Look at unsteady 2D conduction problems including Discretization schemes » Explicit » Implicit Consider the properties of these schemes
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4 Unsteady Diffusion Governing equation: Integrate over control volume and time step
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5 Unsteady Term Write unsteady term in terms of current value (1) and old value (0): Assume: Unsteady term becomes:
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6 Flux Term Consider flux integral Write term as: How to perform integral? Assume flux varies linearly over time step.
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7 Flux Term At each time level, discretize flux term. Current time: Old time:
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8 Source Term Need to evaluate For spatial part, approximate as : Again, assume source varies linearly over time step:
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9 Discrete Equation Set
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University.

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l10 - Lecture 10: A First Look at the Diffusion Equation...

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