Non-Dimensionalization Model

Table of Contents

• 1. Reference Scales
• 2. Primary Converted Quantities
• 3. Field/Coordinate Scaling Conventions
• 5. Practical Notes
• 6. References

PICurv uses a dimensional-input, non-dimensional-core workflow:

1. Users specify physical quantities in YAML.
2. pic.flow converts/control-maps these to non-dimensional solver inputs.
3. Solver evolves non-dimensional fields.
4. Postprocessing can re-dimensionalize outputs for visualization/analysis.

1. Reference Scales

From case.yml:

• L_ref = properties.scaling.length_ref
• U_ref = properties.scaling.velocity_ref
• rho_ref = properties.fluid.density

Derived scales:

• T_ref = L_ref / U_ref
• P_ref = rho_ref * U_ref^2

2. Primary Converted Quantities

Common quantities prepared before solver launch:

• Reynolds number:
  • Re = rho_ref * U_ref * L_ref / mu
  • emitted as -ren
• Physical timestep to non-dimensional timestep:
  • dt* = dt_physical / T_ref
  • emitted as -dt

For file/grid-generated meshes, coordinates are normalized by L_ref before C-side ingestion.

3. Field/Coordinate Scaling Conventions

Representative scaling conventions used across solver/post:

• Position: x* = x / L_ref
• Velocity: u* = u / U_ref
• Pressure: p* = p / P_ref

Particle and Eulerian data follow the same scale family so interpolation/projection remain consistent.

1. End-to-End Flow

• YAML validation and conversion: scripts/pic.flow
• Runtime option ingestion: src/setup.c
• Grid/data read-write scaling hooks: src/io.c
• Post re-dimensionalization trigger via post.yml:
  • global_operations.dimensionalize: true
  • pipeline keyword DimensionalizeAllLoadedFields

5. Practical Notes

• Choose physically meaningful L_ref and U_ref; they directly affect Re and dt*.
• Keep input units consistent across all physical parameters in case.yml.
• For reproducibility, keep run-local generated artifacts under runs/<run_id>/config/.

6. References

• PETSc docs (solver stack context): https://petsc.org/release/docs/manual/
• Config contract details: Configuration Contract (YAML -> Generated Artifacts -> Runtime)