# Define a convection constant vectro!

**URL:** <https://community.freefem.org/t/define-a-convection-constant-vectro/1003>\
**Category:** General Discussion\
**Created:** [June 1, 2021, 3:04pm UTC](https://community.freefem.org/t/define-a-convection-constant-vectro/1003 "2021-06-01T15:04:16Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Kamal\_FEM](https://avatars.discourse-cdn.com/v4/letter/k/a4c791/32.png) [@Kamal\_FEM](https://community.freefem.org/u/Kamal_FEM)\
**Post date:** [June 1, 2021, 3:04pm UTC](https://community.freefem.org/t/define-a-convection-constant-vectro/1003/1 "2021-06-01T15:04:16Z")

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Hi everybody,  
If you allow, I have a question about defining a constant advection vector for my reaction-advection-diffusion system. More precisely, I have the following program where the vector director of the direction of advection is given by the gradient of “c”. My question is to define  
a constant vector [v1,v2] in sorts that the direction is from outside the circle to the part of boundary with the angle between (0,theta). Thank you very much in advance. The program is next:  
real Lx = 3;  
real Ly = 2;  
real dt = 0.05;  
real uf = 1;  
real rhoc = 100;  
// Define mesh boundary  
real theta = pi/10.;  
//real theta2 = 5._pi/11;  
border C(t=0. , theta){x=cos(t); y=sin(t);}  
border D(t=theta , 2.pi){x=cos(t); y=sin(t);}  
// The triangulated domain Th is on the left side of its boundary  
mesh Th = buildmesh(C(150)+D(100));  
//mesh Th = square(60, 40);  
plot(Th);//, ps = “mesh.eps”);  
fespace Uh(Th, P2);  
fespace Vh(Th, P1);  
Uh rho, lrho, rhoold, rhoh, c, ch, cold;  
Vh u1, u2, u, n1, n2, v1, v2, rhop1, cp1;  
rho = rhocexp( -40_(x-Lx/4)^2 - 40\*(y-Ly/2)^2 )

- rhoc_exp( -100_(x-3_Lx/4)^2 - 40_(y-Ly/2)^2 )
- rhoc_exp( -100_(x-0.55_Lx)^2 - 40_(y-Ly/2)^2 );  
Th = adaptmesh(Th, rho);  
//Th = adaptmesh(Th, rho, periodic=[[3,x],[1,x]]);  
plot(Th);  
rho = rho;  
c = rho/rhoc;  
rhoold = rho;  
cold = c;  
// plot (rho, nbiso=50, wait=1);  
//  
problem migr([rho, c], [rhoh, ch]) =  
int2d(Th)(rho_rhoh/dt)  
-int2d(Th)(convect([v1,v2], -dt,rhoold)rhoh/dt)  
+int2d(Th)(dx(v1)rhorhoh+dy(v2)rhorhoh)  
+int2d(Th)(0.01dx(rho)dx(rhoh)+0.01dy(rho)dy(rhoh))  
-int2d(Th)(0.01rho_(rhoc-rhoold)_rhoh)  
+int2d(Th)(c_ch/dt)  
-int2d(Th)(cold\*ch/dt)  
+int2d(Th)(dx(c)\*dx(ch)+dy(c)_dy(ch))  
-int2d(Th)(10_(rho/rhoc-c)\*ch);  
//  
for (int it=0; it\<20; it++) {  
for (int substep=0; substep\<2; substep++){  
//u1 = -dx(cold);  
//u2 = -dy(cold);  
u1 = dx(cold);  
u2 = dy(cold);  
v1 = 0.5 \* u1 \* rhoold/rhoc;  
v2 = 0.5 \* u2 \* rhoold/rhoc;  
migr;  
Th = adaptmesh(Th, rho);  
rho=rho;  
c=c;  
rhoold = rho;  
cold = c;  
}  
// Visu  
rhop1 = rho; cp1 = c;  
plot(Th, rhop1, nbiso=50, fill=0, value=1,  
ps=“migr\_it=”+it+".eps");  
}  
cout \<\< “Done.\n”;