2-D linearised Euler equation
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| - | Problem Definition | + | == 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 p}{\partial t}+\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+M\frac{\partial p}{\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. | ||
| + | == Domain == | ||
| + | [-50,50]*[-50,50] | ||
| + | == Initial Condition == | ||
| + | :<math> p(x,0)=a*exp(-ln(2)*((x-xc)^2+(y-yc)^2)/b^2) </math> | ||
| + | == 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 | ||
| + | [[Image:Nomeanflow.jpg]] | ||
| + | :Mean Flow to left at U=0.5 (c assumed to be 1 m/s) | ||
| + | [[Image:Meanflow.jpg]] | ||
| + | |||
| + | |||
| + | == Reference == | ||
| + | *{{reference-paper|author=Williamson, Williamson|year=1980|title=Low Storage Runge-Kutta Schemes|rest=Journal of Computational Physics, Vol.35, pp.48–56}} | ||
| + | |||
| + | *{{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}} | ||
Latest revision as of 12:31, 19 December 2008
Contents |
Problem Definition
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
Characteristic Boundary Condition
Numerical Method
4th Order Compact scheme in space 4th order low storage RK in time
Results
Pressure
- No mean flow
- Mean Flow to left at U=0.5 (c assumed to be 1 m/s)
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.
