← Shock Tube Lab · Source & validation

Shock Tube Studies

Compare numerical schemes, measure grid convergence, and check the open-system conservation budget. These studies use the same 1D solver as the lab.

Ready. Runs locally in your browser.

γ = 1.4; nondimensional units on x ∈ [0, 1]; transmissive boundaries. First order uses forward Euler (CFL 0.8); MUSCL uses SSP-RK2 (CFL 0.5). The Roe fix uses δ = 0.1ã. Convergence uses 50, 100, 200, 400 and 800 cells.

Grid convergence

L1 errors are cell-center differences from the exact Riemann solution, integrated with Δx. Observed order is log(error ratio) / log(grid ratio). Discontinuities reduce global convergence order even for second-order reconstruction. Failed runs have no error or order.

CellsDensity L1Velocity L1Pressure L1Density orderStatus

Flux × reconstruction

All 12 combinations at the comparison grid and each case's final time. Change one factor at a time to separate the effect of flux from reconstruction. Positivity failures retain their location and time rather than appearing as a successful comparison.

SchemeDensity L1Velocity L1Pressure L1StepsStatus

Mass, momentum & energy budget

For the selected scheme at the comparison grid: change in domain total must equal the time-integrated inflow minus outflow. These are open boundaries, so the domain totals can change. Boundary flux uses the same Euler or RK2 stage weights as the update; the residual should be near floating-point roundoff.

QuantityInitialFinalChangeBoundary integralResidual
Download study CSV