l18 - Lecture 18 Convection and Diffusion(Contd 1 Last Time...

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1 Lecture 18: Convection and Diffusion (Cont’d)
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2 Last Time… Looked at discretizing steady convection-diffusion equation on 2D Cartesian meshes Need face value of to discretize convective term Two different schemes » Central difference scheme (CDS) » Upwind difference scheme (UDS)
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3 This Time … Complete discussion of UDS/CDS schemes Extend CDS/UDS schemes to unstructured meshes Look at accuracy of CDS and UDS schemes Look at false diffusion and dispersion
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4 Upwind Difference Scheme (UDS) Write face value as: “Upwind” in the direction of the mass flow Note asymmetric nature of the discretization!
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5 UDS: Discrete Equation Here What are the signs on the neighbor coefficients? Note extra flow rate term in a P
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6 UDS: Discussion Notice that all coefficients are positive Since for S=0 and extra mass flow rate term =0 » Solution is bounded Scarborough criterion satisfied in the equality for S=0 and extra mass flow rate term=0 Notice extra flow rate term in a P : P nb aa  Zero for continuity- satisfying velocity field
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7 Summary
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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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l18 - Lecture 18 Convection and Diffusion(Contd 1 Last Time...

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