2-D linearised Euler equation

(Difference between revisions)

Latest revision as of 12:31, 19 December 2008

$\frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0$

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

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

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

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.

[-50,50]*[-50,50]

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

Characteristic Boundary Condition

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

Pressure

No mean flow

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

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.

@@ Line 16: / Line 16: @@
 == Results ==
 Pressure
-No mean flow
+:No mean flow
 [[Image:Nomeanflow.jpg]]
-Uniform Mean flow to the left at U=0.5 (speed of sound assumed to be 1)
+:Mean Flow to left at U=0.5 (c assumed to be 1 m/s)
+[[Image:Meanflow.jpg]]
 ==  Reference ==