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ICASE/LaRC workshop on benchmark problems in computational aeroacoustics, category 1, problem 2

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Computer the Numerical solution at t=100,200,300 and 400.Use a domain of [5,450].The boundary condition at r=5 is u(5,t)= sin(:<math>\omega </math> t ).Perform computation for  
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Computer the Numerical solution at t=100,200,300 and 400.Use a domain of [5,450].The boundary condition at r=5 is u(5,t)= sin(<math>\omega </math> t ).Perform computation for  
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a) :<math>\omega =\frac{\pi}{4}</math>
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a) <math>\omega =\frac{\pi}{4}</math>
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b) :<math>\omega =\frac{\pi}{3}</math>
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b) <math>\omega =\frac{\pi}{3}</math>
== Exact Solution ==
== Exact Solution ==
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:<math> u(x,0)=0.5 e^{-(ln 2) (\frac{x -t }{3}) ^2 }</math>
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== Comparison ==
== Comparison ==

Latest revision as of 21:07, 18 February 2007

Solve the initial value problem

 \frac{\partial u}{\partial t} +\frac{u}{r} +\frac {\partial u}{\partial r} =0
 u(x,0)=0


Computer the Numerical solution at t=100,200,300 and 400.Use a domain of [5,450].The boundary condition at r=5 is u(5,t)= sin(\omega t ).Perform computation for a) \omega =\frac{\pi}{4} b) \omega =\frac{\pi}{3}


Exact Solution

Comparison

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