# Homogeneous neumann boundary condition in hydrodynamic stability

I am new to FreeFem++. I am trying to solve for temporal hydodynamic stability of viscous incompressible navier stokes equation for Couette flow.
I have homogeneous neumann boundary condition on pressure on the wall.
here is the code:

complex I = 1i;

real Re;
cout<<“Enter Reynold’s number”<<endl;
cin>>Re;
real om,alp,bet;
// defining the type of stability problem

int a,b;
cout<<“Enter 1 for spatial stability and 2 for temporal stability\n”<<endl;
cin>> a;

if(a==1)
{
cout<<“Enter wave frequency\n”<<endl;
cin>>om;}
else{
cout<<“Enter streamwise wave number\n”<<endl;
cin>>alp;
cout<<“Enter spanwise wave number\n”<<endl;
cin>>bet;}
mesh Th;
int m=500;
Th=square(1,m);
plot(Th,wait=1);

fespace Vh(Th,P2,periodic=[[2,y],[4,y]]);
fespace Mh(Th,P1,periodic=[[2,y],[4,y]]);
fespace Gh(Th,[P2,P2,P2,P1]);
Vh W,u,v,w,a2,a3,Wy,a1;
Mh a4,p;
W=y;

Wy=1;

matrixA1;
matrix B1;

``````              varf A([u,v,w,p],[a1,a2,a3,a4])=int2d(Th)(a1*(I*bet*W+(alp^2+bet^2)/(Re))*u-(1/Re)*dy(a1)*dy(u)+a1*(I*alp)*p+
a2*(I*bet*W+(alp^2+bet^2)/(Re))*v-(1/Re)*dy(a2)*dy(v)+a2*dy(p)+
a3*v*Wy+a3*(I*bet*W+(alp^2+bet^2)/(Re))*w-(1/Re)*dy(a3)*dy(w)+a3*I*bet*p
+a4*I*alp*u+a4*dy(v)+a4*I*bet*w
)+on(1,2,3,4,u=0,v=0,w=0);

varf B([u,v,w,p],[a1,a2,a3,a4])=int2d(Th)(a1*I*u+a2*I*v+a3*I*w);

A1=A(Gh,Gh);
B1=B(Gh,Gh);
ofstream file("A1.csv");
``````

for (int i = 0; i < A1.m; i++) {
for (int j = 0; j < A1.n; j++) {
if(imag(A1(i,j))>0){file<<real(A1(i,j))<<“+”<<imag(A1(i,j))<<“i”;}
else{file<<real(A1(i,j))<<imag(A1(i,j))<<“i”;}
if (j < A1.m - 1) {
file<< “,”;
}
}
file << endl;
}

``````       ofstream file1("B1.csv");
``````

for (int i = 0; i < B1.n; ++i) {
for (int j = 0; j < B1.m; ++j) {
if(imag(B1(i,j))>0){file1<<real(B1(i,j))<<“+”<<imag(B1(i,j))<<“i”;}
else{file1<<real(B1(i,j))<<imag(B1(i,j))<<“i”;}
if (j < B1.m - 1) {
file1<< “,”;
}
}
file1<< endl;
}
While importing the matrices in MATLAB to solve for eigen values i am not getting the result.
Can you help me to find where I have gone wrong?