l22 - Lecture 22: Higher-Order Schemes (Contd) 1 Last Time...

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1 Lecture 22: Higher- Order Schemes (Cont’d)
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2 Last Time… We were looking steady and unsteady convection: Looked at Lax-Wendroff scheme and the consequences of dispersion Started looking at higher-order schemes for the steady convection operator » Upwind-weighted schemes
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3 This Time… We will Complete looking at upwind-weighted schemes Look at how to stabilize unstable higher-order schemes Look at implementation issues
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4 Second-Order Schemes Taylor series about P Truncate Taylor series after second term: Gradient must be written to at least O( x) Fromm Scheme: write gradient as central difference Beam-Warming: write gradient as backward difference Truncation error : O( x 2 )
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5 Gradient Term in Beam-Warming Scheme Second-order scheme: Write gradient as: Combining: Truncation error : O( x) Basis of Beam-Warming scheme
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6 Beam-Warming Scheme Model Equation Start with Integrate over CV, use explicit scheme Use face values based on: Rearrange to obtain   0 0 0 0 31 20 22 PP P W WW u tx     
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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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l22 - Lecture 22: Higher-Order Schemes (Contd) 1 Last Time...

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