l19 - Lecture 19: Convection and Diffusion (Contd) 1 Last...

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1 Lecture 19: Convection and Diffusion (Cont’d)
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2 Last Time … We Looked at CDS/UDS schemes to unstructured meshes Look at accuracy of CDS and UDS schemes Look at false diffusion in UDS using model equation
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3 This Time… We will use model equation to look at behavior of CDS scheme Look at some first-order schemes based on exact solutions to the convection-diffusion equation » Exponential scheme Boundary conditions
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4 CDS Model Equations Pure convection equation: Apply CDS: Expand in Taylor series Do same type of expansion in y direction
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5 Model Equation (Cont’d) Subtract to obtain: Do same in y direction: Substitute into discrete equation Dispersion Term
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6 Discussion Model equation for CDS has extra third-derivative (dispersive) term This type of odd-derivative term tends to cause spatial wiggles Note that truncation error for CDS is O( x 2 ) Thus, UDS is dissipative and CDS is dispersive
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First-Order Schemes Based on Exact
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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.

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l19 - Lecture 19: Convection and Diffusion (Contd) 1 Last...

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