l11 - Lecture 11: Unsteady Conduction Error Analysis 1 Last...

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1 Lecture 11: Unsteady Conduction Error Analysis
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2 Last Time… Looked at unsteady 2D conduction problems Discretization schemes » Explicit » Implicit Considered the properties of this scheme
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3 This Time… Complete unsteady scheme discussion » Properties of Crank-Nicholson scheme Truncation error analysis
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4 Unsteady Diffusion Governing equation: Integrate over control volume and time step
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5 Discrete Equation Set Dropping superscript (1) for compactness Notice old values in discrete equation To make sense of this equation, we will look at particular values of time interpolation factor f (f = 0, 1, 0.5)
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6 Crank-Nicholson Scheme Crank-Nicholson scheme uses f=0.5 t t 1 t 0 0 1 Linear profile assumption across time step
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7 Crank-Nicholson: Discrete Equations Linear equation set at current time level
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8 Properties of Crank-Nicholson Scheme Linear algebraic set at current time level – need linear solver When steady state is reached, P = 0 P . In this limit,
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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-West Lafayette.

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l11 - Lecture 11: Unsteady Conduction Error Analysis 1 Last...

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