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2-D linearised Euler equation

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Problem Definition
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== Problem Definition ==
:<math> \frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0 </math>
:<math> \frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0 </math>
:<math> \frac{\partial v}{\partial t}+M \frac{\partial v}{\partial x}+\frac{\partial p}{\partial y}=0 </math>
:<math> \frac{\partial v}{\partial t}+M \frac{\partial v}{\partial x}+\frac{\partial p}{\partial y}=0 </math>
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:<math> \frac{\partial \rho}{\partial t}+\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+M\frac{\partial \rho}{\partial x}=0 </math>
:<math> \frac{\partial \rho}{\partial t}+\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+M\frac{\partial \rho}{\partial x}=0 </math>
where  M is the mach number , speed of sound is assumed to be 1, all the variabled refer to acoustic perturbations over the mean flow.
where  M is the mach number , speed of sound is assumed to be 1, all the variabled refer to acoustic perturbations over the mean flow.
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:Domain [-50,50]*[-50,50]
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== Domain == [-50,50]*[-50,50]
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:Initial Condition  
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== Initial Condition ==
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:Boundary Condition  
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== Boundary Condition ==
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:Numerical Method  
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== Numerical Method ==
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:Results  
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== Results ==
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:Reference
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==  Reference ==
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*{{reference-paper|author=Williamson, Williamson|year=1980|title=Low Storage Runge-Kutta Schemes|rest=Journal of Computational Physics, Vol.35, pp.48–56}}
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*{{reference-paper|author=Lele, Lele, S. K.|year=1992|title=Compact Finite Difference Schemes with Spectral-like Resolution,” Journal of Computational Physics|rest=Journal of Computational Physics, Vol. 103, pp 16–42}}

Revision as of 02:10, 8 October 2005

Contents

Problem Definition

 \frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0
 \frac{\partial v}{\partial t}+M \frac{\partial v}{\partial x}+\frac{\partial p}{\partial y}=0
 \frac{\partial p}{\partial t}+\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+M\frac{\partial p}{\partial x}=0
 \frac{\partial \rho}{\partial t}+\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+M\frac{\partial \rho}{\partial x}=0

where M is the mach number , speed of sound is assumed to be 1, all the variabled refer to acoustic perturbations over the mean flow. == Domain == [-50,50]*[-50,50]

Initial Condition

Boundary Condition

Numerical Method

Results

Reference

  • Williamson, Williamson (1980), "Low Storage Runge-Kutta Schemes", Journal of Computational Physics, Vol.35, pp.48–56.
  • Lele, Lele, S. K. (1992), "Compact Finite Difference Schemes with Spectral-like Resolution,” Journal of Computational Physics", Journal of Computational Physics, Vol. 103, pp 16–42.
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