2D VPFM Leapfrog Vortex Simulation¶
- Task ID:
physics.vpfm_leapfrog - Domain:
physics - Subdomain:
computational_fluid_dynamics - Status:
test - Tags:
fluid_dynamics,vortex_methods,particle_methods,flow_maps,VPFM,APIC,midpoint_velocity
Public Summary¶
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Example B1 Prompt Excerpt¶
You are a computational fluid dynamics expert. Implement a 2D leapfrog vortex simulation using the **VPFM (Vortex Particle Flow Map)** method in Python. Save the result as `simulation.py` in the current working directory.
Two initial-condition files are provided under the `data/` subdirectory:
data/initial_u_x.npy shape ({{ grid_size_plus_one }}, {{ grid_size }}) float32 — initial horizontal face velocity
data/initial_u_y.npy shape ({{ grid_size }}, {{ grid_size_plus_one }}) float32 — initial vertical face velocity
---
## 1. Grid
- Domain: [0, 1] × [0, 1], bounded
- Boundary conditions: zero normal velocity on all walls; stream function ψ = 0 on boundary (Dirichlet); nodal vorticity = 0 on boundary nodes
Notes¶
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