Example: pipe_flow_validation
Figure 16.3 — Example: Pipe Flow Validation
Crate: cfd-suite (workspace root)
Run: cargo run --example pipe_flow_validation
Source: examples/pipe_flow_validation.rs
What This Example Demonstrates
Validates a cylindrical-pipe FEM simulation against the analytical Hagen-Poiseuille solution (Batchelor 1967 §4.2).
| Concept | API |
|---|---|
| Cylindrical pipe mesh | create_pipe_mesh(R, L, n_circ, n_axial) |
| Stokes solver | StokesFlowProblem, FemConfig |
| Parabolic profile validation | Comparison with v_z(r) = −(dp/dz)R²/4μ·(1 − (r/R)²) |
Key Code Snippet
use cfd_3d::fem::{StokesFlowProblem, StokesFlowSolution};
use cfd_3d::FemConfig;
use cfd_core::prelude::{BoundaryCondition, ConstantPropertyFluid};
// R = 10 mm, L = 100 mm
let pipe_mesh = create_pipe_mesh(0.01, 0.1, 8, 10)?;
let fluid = ConstantPropertyFluid::<f64>::water_20c()?;
let problem = StokesFlowProblem::new(&pipe_mesh, &fluid)?;
let solution = StokesFlowProblem::solve(&problem, &FemConfig::default())?;Theorem Validated
Hagen-Poiseuille (laminar, fully developed, circular pipe):
v_z(r) = −(dp/dz) · R² / (4μ) · (1 − (r/R)²)
Q = π R⁴ (−dp/dz) / (8μ)
The numerical peak velocity at the centreline should match the analytical value to within the FEM discretisation error.