Bluff-body flow at Mach 2, compressible Navier–Stokes, WebGPU. Uniform horizontal inflow ρ = 1, e = 1, vx = 1 from the left. A rectangular body (yellow) is represented by a penalty force fx = −500·vx in the body cells, which damps the velocity inside the body and forces the flow around it. The wake develops a shock structure characteristic of supersonic flow past a blunt obstacle.
Display: density field (blue low → white mid → red high), tuned to ρ ∈ [0.5, 1.5]. The body region is overlaid in yellow.
Equations:
∂ρ/∂t + ∇·(ρv) = 0;
∂(ρv)/∂t + ∇·(ρv⊗v) + ∇p = ∇·σ + f;
∂e/∂t + ∇·(e v) + p∇·v = 0;
p = γe, γ = 0.2; ν = 0.3 h.
Grid: 512² = 262 144 cells. Boundary conditions: inflow (Dirichlet) on the left, zero-gradient on right and top/bottom (free outflow / free-slip).