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Scale-Resolving Simulation at Scale
Certifying High-Order Solver Accuracy with the Isentropic Euler Vortex
- Aerospace
- Energy
What This Simulation Does
The 2d-euler-vortex example transports an analytic isentropic vortex by a uniform background flow across a periodic square domain. Because the exact solution is simply the initial vortex translated in time, any difference between the computed and exact fields is pure numerical error — making this the definitive known-answer test for the order of accuracy and the dispersion/dissipation behavior of a high-order flux-reconstruction scheme.
- Compressible Euler equations — inviscid single-phase ideal gas (γ = 1.4); no viscous terms mask the scheme's intrinsic numerical error
- Closed-form solution — an isentropic vortex of strength S = 13.5, Mach M = 0.4, radius R = 1.5 whose exact evolution is known for all time
- Long-time transport — periodic boundaries let the vortex re-enter the domain, accumulating error so that dispersion and dissipation are measurable with precision
Key Parameters
- Grid: unstructured quadrilateral elements, polynomial order 3; Gauss–Legendre solution and flux points
- Scheme: Rusanov Riemann solver; explicit RK4 time integration
- Vortex: strength S = 13.5, Mach M = 0.4, radius R = 1.5, ideal gas γ = 1.4
- Time: fixed Δt = 5 × 10-3, tend = 100; periodic BCs so the vortex re-enters the domain
The core transferable physics: A smooth, exactly-known flow structure is advected over long distances. What it measures — how quickly a numerical scheme smears (dissipates) and phase-shifts (disperses) a coherent flow feature — is the single most important predictor of whether a solver can carry vortices, acoustic waves, and turbulent eddies across an industrial domain without artificially destroying them.
What Makes This Capability Unique
Exact known-answer benchmark
The analytic solution means error is measured, not estimated. You can prove — not assume — the design order of accuracy of the discretization on your mesh.
Quantifies dispersion & dissipation
Long-time transport isolates exactly how much a scheme smears and phase-shifts a coherent structure — the properties that decide LES and aeroacoustics fidelity.
High-order flux reconstruction
PyFR's flux-reconstruction discretization achieves spectral-like accuracy on unstructured grids — order 3 here, trivially raised to order 5+ to demonstrate p-convergence.
Minutes to a verification report
Launch a mesh-refinement sweep in the browser on enterprise GPUs and produce a convergence table without local installs or HPC procurement.
Domain Applications
Select a domain to see how this simulation applies, with industry-specific scenarios and ROI.
The Problem
Aeroacoustics, LES of turbulent wakes, and rotor/propeller noise all depend on transporting vortices and acoustic waves across large domains without numerical smearing. If the underlying scheme dissipates a vortex before it reaches the far field, the predicted noise signature or wake structure is simply wrong — and no amount of mesh refinement in the wrong solver fixes it economically.
- Certification-grade CFD increasingly requires documented verification & validation (V&V) evidence. Regulators and internal review boards ask for demonstrated order of accuracy before accepting a simulation result in a design decision.
- Community-noise regulations (ICAO, FAA Stage 5) push manufacturers toward simulation-driven low-noise designs where numerical dispersion directly corrupts the predicted tonal content.
The commercial aviation CFD and V&V tooling market exceeds $1B/year, and a single mis-certified aeroacoustic prediction can trigger $10M+ in late-stage redesign.
Applications
| Application | How this simulation maps |
|---|---|
| Aeroacoustic propagation V&V | Vortex transport measures the exact dispersion/dissipation that governs how far a tonal wave survives before the far-field microphone |
| LES wake resolution | Confirms the scheme preserves coherent vortices over many chord lengths before committing to an expensive 3D LES run |
| Solver order-of-accuracy audit | A p- and h-refinement sweep proves the discretization achieves its design order on the target element type |
| Mesh-quality qualification | Reveals how skewed or stretched cells degrade accuracy — before those cells appear in a production mesh |
Quantifiable Business Value
Scenario: An airframer's aeroacoustics group must submit V&V evidence for a new nacelle noise prediction. A documented order-of-accuracy study on the vortex benchmark replaces a months-long ad-hoc verification effort and de-risks a $12M design decision.
Across a full aeroacoustic certification campaign, standardized benchmark V&V typically compresses verification schedules by 6–10 weeks per program.
Recommended Next Steps
Run a convergence study
Execute at successively refined meshes and polynomial orders. Measure the L2 error and confirm the observed slope matches the design order of accuracy.
Characterize dispersion & dissipation
Transport the vortex over many domain lengths and quantify amplitude decay and phase error for your target scheme settings.
Lock in solver settings
Use the verified order and mesh density as the qualified baseline for your production LES or aeroacoustic campaign.
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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