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2-D linearised Euler equation

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== Results ==
== Results ==
Pressure  
Pressure  
-
No mean flow  
+
:No mean flow  
[[Image:Nomeanflow.jpg]]
[[Image:Nomeanflow.jpg]]
 +
:Mean Flow to left at U=0.5 (c assumed to be 1 m/s)
 +
[[Image:Meanflow.jpg]]
Uniform Mean flow to the left at U=0.5 (speed of sound assumed to be 1)
Uniform Mean flow to the left at U=0.5 (speed of sound assumed to be 1)

Revision as of 07:40, 12 November 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

 p(x,0)=a*exp(-ln(2)*((x-xc)^2+(y-yc)^2)/b^2)

Boundary Condition

Characteristic Boundary Condition

Numerical Method

4th Order Compact scheme in space 4th order low storage RK in time

Results

Pressure

No mean flow

Nomeanflow.jpg

Mean Flow to left at U=0.5 (c assumed to be 1 m/s)

Meanflow.jpg Uniform Mean flow to the left at U=0.5 (speed of sound assumed to be 1)

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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