Hello everyone,

I want to analyse the pressure on freefem for a tube

Closed on the left side and open on the right side.

We have 4 boundary conditions for the pressure (look the picture )

À Newman condition “dp/dn=0(on the 3 side 1,2,4 but on the side number 3 we don’t have a Newman boundary condition ) but we have that P(L,t)=0

How we resolute that in freefem with the helmoltz equation can anyone help me please ?

Thanks

This is triaval if you know the Variational form of helmoltz equation

```
int[int] ll=[2,3,4,1]; // to get you label numbering
mesh Th=square(100,10,[x*10,y],label=ll);
fespace Vh(Th,P1);
Vh P,v;
real k = 10;
real k2 = k*k;
macro grad(u) [dx(u),dy(u)] // Def of the grad
func f=1;
solve Helmholtz(P,v) = int2d(Th) ( grad(P)'*grad(v) - k2*P*v)- int2d(Th)(f*v) + on(3,P=0); // 0 on Gamma 3
plot(P,wait=1);
```

This is a stationary cas to make time depend see https://www.um.es/freefem/ff++/pmwiki.php?n=Main.WaveEquation ,

Wifi Propagation for example or

Acoustics

Hello thanks for u respond ,

But why we have f ? And why we have fixed f to 1?

Thanks A lot !

Hello mister ,

Why we don’t need to put the dp/dn on the label 3 please ? Cause we don’t have a Newman bundaty condition on this label.

Best regards

Because it is Homogeneous Neuman Boundary condition this imply the term in variation form.