# Temporal hydrodynamic stability

**URL:** https://community.freefem.org/t/temporal-hydrodynamic-stability/2929
**Category:** General Discussion
**Created:** [February 3, 2024, 5:39pm UTC](https://community.freefem.org/t/temporal-hydrodynamic-stability/2929 "2024-02-03T17:39:15Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![Amitkaush](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/amitkaush/32/1978_2.png) [@Amitkaush](https://community.freefem.org/u/Amitkaush)
#### Post date: [February 3, 2024, 5:39pm UTC](https://community.freefem.org/t/temporal-hydrodynamic-stability/2929/1 "2024-02-03T17:39:15Z")

</div>

Here is the code to calculate temporal hydrodynamic stability for couette flow  
real Mj=0.9; // mach number

complex I = 1i;  
real ga=1.4; //gamma  
real M2=(1/(ga_Mj_Mj));  
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=200;  
real h=1./m;  
Th=square(1,m,[x\*h,y]);  
plot(Th,wait=1);

fespace Vh(Th,P2);  
fespace Mh(Th,P1);  
fespace Gh(Th,[P2,P2,P2]);  
Vh W,u,v,w,a2,a3,Wy,a1;

W=y;

Wy=1;  
plot(W,wait=1);  
real lambda=(10^18);  
matrixA1;  
matrix B1;

```
              varf A([u,v,w],[a1,a2,a3])=int2d(Th)(a1*(I*bet*W+(alp^2+bet^2)/(Re))*u-(1/Re)*dy(a1)*dy(u)+a1*lambda*((alp^2)*u-I*alp*dy(v)+(alp*bet)*w)+
                                                         a2*(I*bet*W+(alp^2+bet^2)/(Re))*v-(1/Re)*dy(a2)*dy(v)-a2*I*lambda*(alp*dy(u)+bet*dy(w))-lambda*dy(a2)*dy(v)+
                                                         a3*v*Wy+a3*(I*bet*W+(alp^2+bet^2)/(Re))*w-(1/Re)*dy(a3)*dy(w)+a3*lambda*((alp*bet)*u-I*bet*dy(v)+(bet^2)*w)
                                                         
                                                     )+on(1,3,u=0,v=0,w=0);
                                                         
                                                         
              varf B([u,v,w],[a1,a2,a3])=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;  
}  
cout\<\<A1.m\<\<endl;  
cout\<\<A1.n\<\<endl;  
Is the way i defined the mesh and define varf is correct?