Monitoring runs

During a simulation x3d2 writes global scalar quantities to a monitoring.csv file at every output step (controlled by n_output in the input file). This file is useful for tracking the evolution of the flow and for comparison with reference data.

Output format

The file is a comma-separated CSV with a header line:

# time, enstrophy, div_u_max, div_u_mean

Each subsequent row contains one record per output step.

Quantities

Column	Description	Formula
time	Simulation time	\(t\)
enstrophy	Spatially-averaged enstrophy	\(\mathcal{E} = \frac{1}{2N} \sum |\nabla \times \mathbf{u}|^2\)
div_u_max	Maximum of \(|\nabla \cdot \mathbf{u}|\)	Divergence-free check
div_u_mean	Mean of \(|\nabla \cdot \mathbf{u}|\)	Divergence-free check

Note

The divergence columns (div_u_max and div_u_mean) measure how well the incompressibility constraint \(\nabla \cdot \mathbf{u} = 0\) is satisfied. Since x3d2 enforces the incompressibility constraint via a pressure projection, these values should remain close to machine precision (typically \(\sim 10^{-14}\) in double precision). A growing divergence indicates a problem with the pressure solver or time-stepping stability.

Example: plotting with Python

import pandas as pd
import matplotlib.pyplot as plt

columns = ["time", "enstrophy", "div_u_max", "div_u_mean"]
df = pd.read_csv("monitoring.csv", comment="#", names=columns)

fig, axes = plt.subplots(3, 1, figsize=(8, 8), sharex=True)

axes[0].plot(df["time"], df["enstrophy"])
axes[0].set_ylabel("Enstrophy")

axes[1].plot(df["time"], df["div_u_max"])
axes[1].set_ylabel("div(u) max")

axes[2].plot(df["time"], df["div_u_mean"])
axes[2].set_ylabel("div(u) mean")

axes[-1].set_xlabel("Time")

plt.tight_layout()
plt.savefig("monitoring.png")