[Nico994396]

Dear all,
i'm developing a solver for the Compressible Euler Equations by using explicit Runge-kutta 4 scheme.


In particular, i've followed the approach of the following paper:
"On the implementation of low-dissipative Runge–Kutta projection
methods for time dependent flows using OpenFOAM" by V. Vuorinen a, ⇑ , J.-P. Keskinen a , C. Duwig b , B.J. Boersma.


Even tough i write the code ( sorry if it seems that it is not compact, but it was a test ), it seems that the method is not stable:
Indeed, i tested the solver with an atmosphere in equilibrum ( i used the potential temperature to initialize the field ), and even tough i use very small time steps, during the time evolution waves are created ( if the solver is balanced the atmosphere should remain at rest ).
You can find an image of what happens during the simulation ( the image shows that pressure-waves are created) and you'll find my solver.
If someone can give an explanation about that i will be greatfull.
Thank you.


Strange-wave-behabviour.png

EulerRK4Foam.C

correctBoundaryRho.H