Shock Tube Lab

x = 0tube view: density, scheme A · dashed line = diaphragmx = 1

Results at the final time

Scheme	L1 error (density)	Steps	Run time	Cells across shock	Cells across contact	Status

Cells across a discontinuity counts cells inside the 5–95% band of the jump (shock measured in p, contact in ρ), for cases with a left fan and a right shock. Run time is measured in this browser.

This run against the references

Quantity	This run	Reference	Difference	Check

Repository results, 96 × 144 grid, HLL + van Leer

M∞	Standoff Δ/R	Billig	Difference	p₀/p∞	Pitot (exact)	Difference

From results/blunt_body.md. The finer grid takes minutes in Python, so the browser runs coarser grids; the standoff is grid-independent to within about 1% (0.703, 0.701, 0.697 on 32 × 48, 64 × 96, 128 × 192 at M = 3).

Steady 2D Euler equations, γ = 1.4, on a body-fitted polar grid over the windward half of a unit cylinder (radial cells clustered at the wall). Slip wall, free stream on the outer arc, supersonic outflow on the plane x = 0. Standoff is read where the stagnation-line pressure crosses the midpoint between the free-stream and normal-shock values; stagnation pressure is extrapolated to the wall. References: Billig (1967) correlation Δ/R = 0.386 exp(4.67/M²) and the exact Rayleigh pitot formula. This tab is a line-by-line JavaScript port of src/shocktube/blunt2d.py; at M = 3 it reproduces the repository's grid-study values (Δ/R = 0.703 and 0.701, p₀/p∞ = 12.030 and 12.026 on 32 × 48 and 64 × 96). It also stops a run once the standoff and stagnation pressure stop changing, because a limited scheme's residual can plateau above the tolerance. Built by Badr Elsayed.