Example: fem_3d_stokes
Figure 10.3 — Example: FEM 3D Stokes
Crate: cfd-suite (workspace root)
Run: cargo run --example fem_3d_stokes
Source: examples/fem_3d_stokes.rs
What This Example Demonstrates
Solves the creeping (Stokes) flow equations in a unit-cube lid-driven cavity using P1/P1 stabilised tetrahedral finite elements.
| Concept | API |
|---|---|
| Constant-property fluid | ConstantPropertyFluid::<f64>::water_20c() |
| Cube mesh via Kuhn triangulation | create_refined_cube_mesh(nx) |
| FEM problem + solver | StokesFlowProblem, FemSolver, FemConfig |
| Boundary conditions | BoundaryCondition::NoSlip, BoundaryCondition::Dirichlet |
Key Code Snippet
use cfd_3d::fem::{FemConfig, FemSolver, StokesFlowProblem};
use cfd_core::physics::fluid::ConstantPropertyFluid;
let fluid = ConstantPropertyFluid::<f64>::water_20c()?;
// ρ = 998.2 kg/m³, μ = 1.002e-3 Pa·s
println!("ν = {:.2e} m²/s", fluid.viscosity / fluid.density);
let mesh = create_refined_cube_mesh(5)?; // 5×5×5 → 125 verts, ~500 tets
let problem = StokesFlowProblem::new(&mesh, &fluid)?;
let solution = FemSolver::solve(&problem, &FemConfig::default())?;Physics Background
The Stokes equations are the zero-inertia limit of Navier-Stokes:
−∇p + μ ∇²u = 0, ∇·u = 0
These are linear, making FEM solution direct (one linear system). They are the correct model when Re ≪ 1 (microfluidics, polymer processing, geophysical creeping flows). Reference geometry: Ghia et al. (1982).