Computational art and PDE visualization on word-shaped cutout domains with FEniCSx, Gmsh, and PyVista.

Alphaflow builds meshes with letters removed as true interior voids, solves a selected PDE on the resulting domain, and renders the result as a high-resolution image. It is intended for expressive geometry-aware visualization, not as a validated solver package.

Use an existing Python environment that already has a working FEniCSx stack. The active environment should provide:

• dolfinx
• mpi4py
• petsc4py
• gmsh

Install Alphaflow into that environment:

python -m pip install -e .[meshing,dev]

If gmsh.py is installed in a non-standard location, set one of:

• ALPHAFLOW_GMSH_PY=/path/to/gmsh.py
• ALPHAFLOW_GMSH_SITEPACKAGES=/path/to/site-packages

Build a mesh:

python scripts/build_word_mesh.py ALPHAFLOW --output-dir outputs

Render flow:

python scripts/render_flow_logo.py ALPHAFLOW --output-dir outputs

Render elasticity:

python scripts/render_elasticity_logo.py ALPHAFLOW --output-dir outputs

Render Helmholtz:

python scripts/render_helmholtz_logo.py ALPHAFLOW --output-dir outputs --obstacle-bc sound-soft

You can also use the installed CLI:

alphaflow build-mesh ALPHAFLOW --output-dir outputs
alphaflow flow ALPHAFLOW --output-dir outputs
alphaflow elasticity ALPHAFLOW --output-dir outputs
alphaflow helmholtz ALPHAFLOW --output-dir outputs --obstacle-bc sound-soft

These are the exact commands used to generate the versioned gallery images in docs/readme_assets/.

Flow:

python scripts/render_flow_logo.py ALPHAFLOW \
  --output-dir outputs/readme_alphaflow_flow \
  --width 20.0 \
  --height 3.6 \
  --mesh-size 0.18 \
  --obstacle-mesh-size 0.08 \
  --letter-spacing 0.04 \
  --nu 0.08 \
  --inflow-speed 0.7 \
  --background light-blue

Elasticity:

python scripts/render_elasticity_logo.py ALPHAFLOW \
  --output-dir outputs/readme_alphaflow_elasticity \
  --width 20.0 \
  --height 3.6 \
  --mesh-size 0.18 \
  --obstacle-mesh-size 0.08 \
  --letter-spacing 0.04 \
  --young-modulus 150.0 \
  --traction-y -0.02 \
  --warp-scale 3.2

Helmholtz:

python scripts/render_helmholtz_logo.py ALPHAFLOW \
  --output-dir outputs/readme_alphaflow_helmholtz \
  --width 20.0 \
  --height 3.6 \
  --letter-spacing 0.04 \
  --degree 4 \
  --wavenumber 4.8 \
  --obstacle-bc sound-soft \
  --source-x-fraction 0.14 \
  --source-y-fraction 0.68 \
  --source-sigma-fraction 0.032

• scripts/build_word_mesh.py: build and preview a cutout mesh
• scripts/render_flow_logo.py: solve the steady flow example and render streamlines
• scripts/render_elasticity_logo.py: solve the linear elasticity example and render bending
• scripts/render_helmholtz_logo.py: solve the Helmholtz example and render the acoustic field

The mesh uses these physical groups:

• fluid: 2D cells of the domain
• inlet: left boundary
• outlet: right boundary
• walls: top and bottom boundaries
• obstacle: letter boundaries

Current PDE setups:

• flow: parabolic inflow, no-slip walls and letters, zero-pressure outlet
• elasticity: clamped left edge, traction-loaded right edge
• Helmholtz: absorbing left/right boundaries, sound-hard top/bottom walls, selectable sound-hard, sound-soft, or impedance letter BCs

Shared geometry options:

• --width
• --height
• --mesh-size
• --obstacle-mesh-size
• --x-offset
• --letter-spacing

Flow:

• --nu
• --inflow-speed
• --background

Elasticity:

• --young-modulus
• --poisson-ratio
• --traction-y
• --warp-scale
• --show-undeformed

Helmholtz:

• --degree
• --wavenumber
• --obstacle-bc
• --impedance
• --source-amplitude
• --source-x-fraction
• --source-y-fraction
• --source-sigma-fraction

• screenshots default to 3600 x 1440
• planar views are framed so the domain diagonal occupies about 90% of the image diagonal
• flow streamlines are seeded directly on the inlet boundary
• flow backgrounds support soft-gray, mist, and light-blue

• This repo uses Gmsh-based meshing, not meshr.
• Generated files go to outputs/ by default, and outputs/ is gitignored.
• Some XDMF writes may emit HDF5 warnings depending on the local FEniCSx / HDF5 build; current workflows still complete and write usable files.
• The Helmholtz path defaults to polynomial degree 4 to reduce low-order pollution effects.