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Tutorial: lid-driven cavity ​

The classic incompressible-flow benchmark. A unit square is filled with fluid; the top wall (the "lid") slides at u = 1 m/s while the other three walls are no-slip. The shear dragged in by the lid drives one large recirculating vortex. Density 100 and dynamic viscosity 1 give a Reynolds number Re = ρUL/μ = 100. Every number below comes from a real run against Kratos 10.4.

You can hand the whole thing to an assistant:

Set up a lid-driven cavity: a 1×1 m box of fluid (density 100, viscosity 1), the top wall moving at 1 m/s, the others no-slip. Run it and show me the velocity field.

A smaller, literal, pre-verified version is the kratos://examples/lid-driven-cavity resource, and notebooks/fluid_cavity.ipynb walks through this exact case as a live MCP client.

1. Generate the mesh ​

A coarse 10×10 unit square of triangles (the monolithic VMS solver wants a simplex mesh). No load conditions are needed — the walls are nodal velocity constraints.

json
mdpa_create_structured_mesh({
  "path": "/tmp/cavity/mesh.mdpa",
  "kind": "rectangle", "size": [1.0, 1.0], "divisions": [10, 10],
  "element_name": "Element2D3N", "triangles": true
})
→ { "num_nodes": 121, "num_elements": 200 }

The pressure in an all-walls cavity is only defined up to a constant, so one node must pin it. The structured generator makes left/right/bottom/top sub-model-parts but not a single-node one, so the shipped example adds a corner sub-model-part holding just the lower-left node (see the example files).

2. Scaffold the case ​

The fluid_transient template is monolithic Navier–Stokes (VMS). Point it at the cavity fluid properties:

json
create_project({
  "directory": "/tmp/cavity", "template": "fluid_transient", "name": "cavity",
  "overrides": { "density": 100.0, "dynamic_viscosity": 1.0,
                 "volume_part": "domain", "skin_parts": ["left","right","bottom","top"] }
})

3. Apply the walls and the moving lid ​

No-slip (zero velocity) on three walls, the lid velocity on the top, and the pressure pin on the corner:

json
add_boundary_condition({ "parameters_file": ".../ProjectParameters.json",
  "kind": "fix_velocity", "model_part": "FluidModelPart.left", "value": [0,0,0] })
// ...same for FluidModelPart.right and FluidModelPart.bottom...
add_boundary_condition({ "parameters_file": ".../ProjectParameters.json",
  "kind": "inlet_velocity", "model_part": "FluidModelPart.top", "value": [1.0, 0, 0] })
add_boundary_condition({ "parameters_file": ".../ProjectParameters.json",
  "kind": "outlet_pressure", "model_part": "FluidModelPart.corner", "value": 0.0 })

4. Run ​

json
run_simulation({ "case_dir": "/tmp/cavity", "wait_seconds": 60 })
→ { "state": "succeeded", "elapsed_seconds": 1.0 }

Thirty pseudo-time steps march the impulsively-started lid to a steady vortex.

5. Check the recirculation ​

Read the velocity on the vertical centerline (x = 0.5). The signature of the vortex is that the interior velocity reverses: fluid dragged forward under the lid returns backward through the cavity.

lid velocity u on the top row .................. 1.00 m/s (imposed)
centerline u(y) at x = 0.5, minimum ............ -0.116 m/s at y = 0.40

On a fine (Ghia) mesh at Re = 100 that minimum is about −0.21 at y ≈ 0.46; this coarse 10×10 mesh under-resolves the vortex core (expected — refine the mesh for a sharper profile).

6. Preview ​

json
results_render({ "file": ".../vtk_output/FluidModelPart_0_30.vtk",
                 "variable": "VELOCITY", "camera": "xy", "show_edges": true })

Colouring by velocity magnitude from a top-down camera shows the bright lid-driven shear band along the top and the slow vortex core below. results_animate over the snapshots shows the vortex spinning up from rest.

Variations ​

  • Higher Reynolds number — raise the velocity or lower the viscosity; at Re ≳ 1000 secondary corner eddies appear (and you'll want a finer mesh).
  • Finer mesh — divisions: [40, 40] sharpens the centerline profile toward the Ghia benchmark.
  • Fractional-step solver — the fluid_fractional_step template solves the same case with a cheaper pressure-splitting scheme (see kratos://examples/channel-flow).