2-D linearised Euler equation

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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