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Stress-Testing Shock Capturing with Double Mach Reflection
- Aerospace
- Energy
- Oil & Gas
What This Simulation Does
The 2d-double-mach-reflection example drives a strong Mach 10 shock into an inclined wall, generating the canonical double Mach reflection pattern: incident and reflected shocks, a Mach stem, a slip line, and a triple point. It is one of the most demanding stress tests for shock capturing in high-order solvers.
- Compressible Euler equations — inviscid single-phase ideal gas (γ = 1.4) with entropy-filter shock capturing
- Entropy filter — enforces a discrete minimum-entropy principle, keeping the high-order solution positive and oscillation-free across the Mach-10 shock
- Moving-shock boundary — a time-dependent moving-shock condition on the top boundary reproduces the classic setup exactly
Key Parameters
- Grid: quadrilateral elements, polynomial order 3; Gauss–Legendre points
- Post-shock state (ρ, u, v, p) = (8.0, 7.145, −4.125, 116.5) vs ambient (1.4, 0, 0, 1.0)
- Scheme: HLLC Riemann solver; entropy filter (2 iterations); explicit RK4
- Time: fixed Δt = 5 × 10-6, tend = 0.2
The core transferable physics: A strong shock reflects off a surface and produces complex shock–shock interactions. Whether a solver can capture these sharp discontinuities without spurious oscillations — while preserving positivity of density and pressure — determines whether it can be trusted on supersonic inlets, blast loading, and high-pressure valve flows.
What Makes This Capability Unique
Entropy-filter shock capturing
A provably positivity-preserving, minimum-entropy filter keeps high-order accuracy in smooth regions while cleanly capturing Mach-10 discontinuities.
HLLC Riemann resolution
The HLLC solver resolves the contact/slip line and the triple point sharply — the structures that carry the physics of shock-focusing loads.
High-order in smooth regions
Unlike low-order shock solvers, high-order flux reconstruction keeps smooth-region accuracy so peak loads and wave arrival times are not smeared.
Robust at extreme Mach
A stable Mach-10 result on a browser-launched GPU run demonstrates the solver is ready for hypersonic and blast-class problems.
Domain Applications
Select a domain to see how this simulation applies, with industry-specific scenarios and ROI.
The Problem
Hypersonic vehicles, supersonic inlets, and store-separation events are dominated by strong shock reflections and shock–shock interactions. The Mach stem and triple point that form in a double Mach reflection are the same structures that create localized pressure and heating spikes on real airframes — and mis-predicting them can mean structural or thermal-protection failure.
- Shock–boundary-layer and shock–shock interaction drives peak heating on inlets and control surfaces; low-order smearing hides these hot spots.
- Wind-tunnel testing at Mach 10 is scarce and costs $50K–$200K per run; validated shock-capturing CFD offsets many of these.
Global hypersonics R&D exceeds $5B/year, and TPS redesign after a missed heating prediction can cost $10M+.
Applications
| Application | How this simulation maps |
|---|---|
| Hypersonic inlet shock train | Reflected-shock and Mach-stem structure maps directly to inlet compression; predicts peak pressure and heating locations |
| Control-surface shock impingement | Triple-point loading indicates where localized heating and pressure spikes hit deflected surfaces |
| Store / stage separation | Moving-shock interactions between bodies validated before expensive coupled 6-DOF runs |
| TPS sizing | Sharp shock capture yields the peak heat flux needed to size thermal protection with less margin |
Quantifiable Business Value
Scenario: A hypersonics team validates shock-capturing fidelity on this benchmark, then replaces several Mach-10 wind-tunnel entries with GPU CFD and sizes TPS with tighter, evidence-based margins.
Lighter, evidence-based TPS margins add range/payload worth far more than the direct test savings over a vehicle program.
Recommended Next Steps
Confirm shock-capturing fidelity
Run the benchmark and verify the Mach stem, slip line, and triple point are sharp and oscillation-free at your target resolution.
Sweep shock strength
Vary the incident Mach number and wall angle to bracket your application's reflected-shock loads.
Apply to your geometry
Carry the verified entropy-filter settings into a simulation of your inlet, vent, or valve to predict peak loads.
Ready to Run This Simulation?
Run this example on SRS's cloud platform. No installation, no infrastructure management — just results.
For questions or to schedule a technical briefing, contact the SRS simulation team.
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