# cfdCode cpp 1D Diffusion Equation

Published on: 02 April 2024

- source file

```
#include <iostream>
#include <fstream>
#include <vector>
#include <cmath>
#include "gnuplot-iostream.h"
using namespace std;
int main() {
Gnuplot gp;
int nx = 41;
double dx = 2.0 / (nx - 1);
int nt = 20;
double nu = 0.3;
double k = 0.2;
double dt = k * pow(dx, 2) / nu;
vector<double> u(nx, 1.0);
for (int i = int(0.5 / dx); i <= int(1 / dx); i++) {
u[i] = 2.0;
}
vector<double> un(nx, 1.0);
for (int n = 1; n <= nt; n++) {
un = u;
for (int i = 1; i < nx - 1; i++) {
u[i] = un[i] + nu * dt / pow(dx, 2) * (un[i+1] - 2 * un[i] + un[i-1]);
}
}
ofstream outfile("output.dat");
for (int i = 0; i < nx; i++) {
outfile << i * dx << " " << u[i] << "\n";
}
outfile.close();
gp << "set title 'x vs u graph'\n";
gp << "set xlabel 'x'\n";
gp << "set ylabel 'u'\n";
gp << "set grid\n";
gp << "set xtics rotate by 90 right\n";
// gp << "set term png\n";
// gp << "set output 'sample-csv.png'\n";
gp << "plot('output.dat') using 2:xticlabel(1) with linespoints\n";
return 0;
}
```

copy the text from above link, paste it in a text file, save this file with extension ".h" as "gnuplot-iostream.h" in the same folder of the source code.