# Plot u vs x for fixed t and y

**URL:** https://community.freefem.org/t/plot-u-vs-x-for-fixed-t-and-y/4152
**Category:** General Discussion
**Created:** [December 11, 2025, 2:10pm UTC](https://community.freefem.org/t/plot-u-vs-x-for-fixed-t-and-y/4152 "2025-12-11T14:10:06Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![ahmed2018](https://avatars.discourse-cdn.com/v4/letter/a/b4bc9f/32.png) [@ahmed2018](https://community.freefem.org/u/ahmed2018)
#### Post date: [December 11, 2025, 2:10pm UTC](https://community.freefem.org/t/plot-u-vs-x-for-fixed-t-and-y/4152/1 "2025-12-11T14:10:06Z")

</div>

In this runnable code, I want to either **plot u versus x** for a fixed y and time t, or **extract the u vs x data**. What should I add to this code to achieve that?  
// thermal\_convection.edp  
//  
// Discussion:  
//  
// Forced + Natural heat convection in a pipe  
// Navier−Stokes equations + convection−diffusion on temperature  
//  
// Licensing:  
//  
// This code is distributed under the MIT license.  
//  
// Modified:  
//  
// 26 June 2015  
//  
// Author:  
//  
// Florian De Vuyst  
//  
// Reference:  
//  
// Florian De Vuyst,  
// Numerical modeling of transport problems using freefem++ software -  
// with examples in biology, CFD, traffic flow and energy transfer,  
// HAL id: cel-00842234  
// [Numerical modeling of transport problems using freefem++ software -- with examples in biology, CFD, traffic flow and energy transfer - CEL - Cours en ligne](https://cel.archives-ouvertes.fr/cel-00842234)  
//  
cout \<\< “\n”;  
cout \<\< “thermal\_convection():\n”;  
cout \<\< " FreeFem++ version\n";  
cout \<\< " Thermal convection and diffusion by Navier-Stokes flow.\n";  
//  
// Define the boundary lines.  
//  
real lx = 0.25;  
real Lx = 3.0;  
real Ly = 1.0;

border c1 (t=0.0, lx) {x = t; y = 0.0;}  
border c2 (t=lx, Lx-lx) {x = t; y = 0.0;}  
border c3 (t=Lx-lx,Lx) {x = t; y = 0.0;}  
border c4 (t=0.0,Ly) {x = Lx; y = t;}  
border c5 (t=Lx,0.0) {x = t; y = Ly;}  
border c6 (t=Ly,0.0) {x = 0.0; y = t;}  
//  
// Define the mesh.  
//  
mesh Th = buildmesh ( c1(10) + c2(200) + c3(10) + c4(30) + c5(100) + c6(30) );  
//  
// Plot the mesh.  
//  
plot ( Th, wait = false, ps = “thermal\_convection\_mesh.ps” );  
//  
// Define the finite element spaces:  
// UH for velocity fields,  
// XH for pressure P, temperature THETA, and specific volume TAU.  
//  
fespace Uh(Th, P1b );  
Uh u, v, uold, vold, uh, vh;  
fespace Xh(Th, P1 );  
Xh p, ph;  
Xh theta, thetaold, thetah;  
Xh tau;  
//  
// Initialize the fields.  
//  
real uin0 = 0.2;  
func uin = uin0 \* 4.0 \* (y/Ly) \* (1.0-y/Ly);  
u = uin;  
uold = u;  
v = 0.0;  
vold = v;

real thetain = 20.0;  
theta = thetain;  
thetaold = theta;  
//  
// Define the weak form of the heat equation.  
//  
real dt = 0.05;  
real heatflux = 100.0;  
real kappa = 0.001;

problem HeatStep ( theta, thetah ) =  
int2d (Th) ( theta \* thetah / dt )

- int2d (Th) ( convect ([u,v], -dt, thetaold)\*thetah/dt )

- int2d (Th) ( kappa \* dx(theta) \* dx(thetah) + kappa \* dy(theta) \* dy(thetah) )

- int1d (Th, c2) ( kappa \* heatflux \* thetah )

- on ( c6, theta = thetain );  
//  
// Define the weak form of the Navier Stokes equations.  
//  
real gravity = 9.81;  
real nu = 0.001;

problem NavierStokesStep ( [u, v, p], [uh, vh, ph] ) =  
int2d (Th) ( u \* uh / dt )

- int2d (Th) ( convect ( [uold, vold], -dt, uold ) \* uh/dt )

- int2d (Th) ( nu \* dx(u) \* dx(uh) + nu \* dy(u) \* dy(uh) )
- int2d (Th) ( tau \* dx(p) \* uh )
- int2d (Th) ( v \* vh / dt )

- int2d (Th) ( convect ([uold, vold], -dt, vold) \* vh / dt )

- int2d (Th) ( nu \* dx(v) \* dx(vh) + nu \* dy(v) \* dy(vh) )
- int2d (Th) ( tau \* dy(p) \* vh )
- int2d (Th) ( gravity \* vh )
- int2d (Th) ( dx(u) \* ph + dy(v) \* ph )
- on ( c6, u=uin, v=0 )
- on ( c1, c2, c3, c5, u=0, v=0 );  
//  
// Time steps  
//  
real cst = 1.0;  
real dtsnap = 0.5;  
real t = 0.0;  
real ttosnap = 2.0;

for ( int it = 1; it \<= 100; it++ )  
{  
t = it \* dt;  
cout \<\< it \<\< " T = " \<\< t \<\< “\n”;

HeatStep;

thetaold = theta;  
tau = cst \* theta;

NavierStokesStep;

uold = u;  
vold = v;

plot ( [u, v], theta, nbiso = 80, value = false );

if ( ttosnap \<= t )  
{  
cout \<\< " Plotting T = " \<\< t \<\< “\n”;  
ttosnap = ttosnap + dtsnap;  
plot ( [u,v], theta, nbiso = 80, value = false,  
ps = “thermal\_convection\_”+it+“.ps”,  
cmm = "Step “+it );  
}  
}  
//  
// Terminate.  
//  
cout \<\< “\n”;  
cout \<\< “thermal\_convection():\n”;  
cout \<\< " Normal end of execution.\n”;

exit ( 0 );