l20 - Lecture 20: Unsteady Convection 1 Last Time Looked at...

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1 Lecture 20: Unsteady Convection
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2 Last Time… Looked at model equation to examine dispersive behavior of CDS scheme Look at a first-order scheme based on exact solutions to the convection-diffusion equation » Exponential scheme Looked at boundary conditions
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3 This Time… We will Develop more insight into the behavior of the convection operator by looking at unsteady convection Consider the stability of implicit and explicit time- differencing schemes for » CDS » UDS Consider the corresponding model equations and try to explain the observed behavior
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4 Unsteady Convection Equation For simplicity, consider linear wave equation Consider 1-D domain of length L=1. Initial condition: Solution: How well do our numerical schemes capture this? Convection-diffusion equation with =0, =1, u=constant Traveling wave
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5 Wave Forms Sine Wave Square Wave For u>0, profiles shift to the right by (ut) in time t. For u=1 and t=0.25, the shift is 0.25 units
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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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l20 - Lecture 20: Unsteady Convection 1 Last Time Looked at...

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