A flow solver built to be differentiated

One site, four depths

Read at the depth you need

Every page starts with a one-minute summary. Passages deeper than your dial fold into a labelled stub that you can open in place. Set the dial here or in the top bar; it follows you across the site.

1. Level 1 Essentials What it is and why it matters For anyone
2. Level 2 Practice How to use it For users and MDO integrators
3. Level 3 Mechanics How it works: algorithms and architecture For developers
4. Level 4 Theory Derivations, proofs and numerical analysis For numerical analysts

Reading paths

Start from who you are

Each path is an ordered walk through the documentation and sets a suggested depth. You can leave a path or move the dial at any time.

• MDO integrator

  You wrap Gyre as a discipline in an optimization framework and need its interface, its derivatives and evidence that they are right.

  Suggested depth: L2 Practice
  1. What Gyre is
  2. Integrating with an MDO framework
  3. Gradients and error estimates
  4. Coupled aero-structural adjoint
  5. Inside OpenMDAO
  6. Linearisation and gradients
  7. Discipline contract
  8. Adjoints and sensitivities
  Start this path

• CFD practitioner

  You want to set up, run and judge flow solutions, and to know what the solver can and cannot do.

  Suggested depth: L2 Practice
  1. Capabilities and limits
  2. Getting started
  3. Cases
  4. Mesh files
  5. Inviscid aerofoil
  6. Transonic aerofoil
  7. Laminar cylinder
  8. Turbulent flat plate
  9. Sphere in three dimensions
  10. A mesh from Gmsh
  11. Verification
  Start this path

• Solver developer

  You change the code and need to know how it is organised, how the kernels are written and how changes are tested.

  Suggested depth: L3 Mechanics
  1. Architecture at a glance
  2. Design decisions
  3. Code structure
  4. Differentiable programming patterns
  5. Testing strategy
  6. Development process
  7. Authoring guide
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• Numerical analyst

  You want the equations, the discretization and the proofs, and the verification studies that test them.

  Suggested depth: L4 Theory
  1. Governing equations
  2. Split-form DG spectral elements
  3. Two-point and interface fluxes
  4. Viscous terms — the BR2 scheme
  5. Turbulence closure (RANS, Spalart–Allmaras)
  6. Implicit solver
  7. Adjoints and sensitivities
  8. Output error estimation
  9. Order of accuracy
  10. Turbulence closure
  Start this path

• Operator

  You deploy and run the service for others on a tailnet, and need to know what is running and whether it is healthy.

  Suggested depth: L2 Practice
  1. Deployment
  2. Service API
  3. Service architecture
  4. Pipelines and provenance
  5. Performance
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• AI agent

  You are, or you operate, an agent that drives Gyre through its tool interface. Start from llms.txt; every page is also served as Markdown.

  Suggested depth: L2 Practice
  1. Agent interface (MCP)
  2. An agent at work
  3. MCP tool reference
  4. REST API reference
  5. Case schema
  6. Mesh files
  7. Pipelines
  Start this path

Capabilities

What Gyre is built to do

• Differentiable by construction

  The numerical kernels are pure JAX functions, so Jacobian products, adjoints and shape sensitivities come from automatic differentiation of the same code that computes the flow.

  Read more →

• High-order, entropy-conservative volume terms

  Split-form discontinuous-Galerkin spectral elements on curved meshes, with entropy-conservative two-point fluxes. A discrete entropy inequality is proven for the two entropy-stable interface fluxes (matrix dissipation in entropy variables, and Lax–Friedrichs); the default classical Roe flux is dissipative in the verification study.

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• Exact adjoints, through shocks and turbulence

  One transposed solve per output gives derivatives with respect to flow conditions and every surface node, in two and three dimensions; shock capturing and the turbulence closure, wall distance included, are part of the linearisation.

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• A discipline, not an optimizer

  A framework-neutral contract — solve, outputs, loads and displacements, forward and reverse products — that an MDO framework wraps, locally or over the network.

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• Service, pipelines and agents

  One deployable unit serves a REST API with warm sessions, declarative pipelines, a Model Context Protocol endpoint, and this documentation stamped with the running revision.

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• Evidence with provenance

  Verification pages render the output of the verification suite; every chart and table names the revision, time and device that produced it.

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Contents

71 pages in 7 sections

• Overview What Gyre is, where it sits in a design-optimization stack, how it is put together, and what it does not do. 4 pages · up to L3
• User Guide How to install Gyre, describe a case, bring your own mesh, run it from the command line, the service or Python, obtain gradients and error estimates, wire it into an MDO framework or an agent, and deploy it. 12 pages · up to L4
• Examples Worked cases with real output: an inviscid aerofoil, a transonic flow with shocks, a separated viscous flow, a turbulent boundary layer, a sphere in three dimensions, a case on a mesh imported from Gmsh, a warm-started polar with adjoint slopes, a coupled aero-structural adjoint, OpenMDAO, and an agent session. 12 pages · up to L3
• Verification Every numerical claim in this documentation is backed by an executable study. The studies run as a pipeline, write machine-readable results with provenance, and the charts and tables on these pages are rendered from those files. 12 pages · up to L4
• Software Engineering How the capability is built: design decisions and their costs, the differentiable-programming patterns the solver relies on, code structure, the service architecture, testing, pipelines and provenance, performance, and process. 10 pages · up to L4
• Mathematics & Numerical Methods The equations Gyre solves and the numerical methods it uses — split-form DG spectral elements, entropy-conservative fluxes, curvilinear metrics, BR2 viscous terms, the Spalart–Allmaras turbulence closure, shock capturing, the implicit solver, adjoints and output error estimation — with derivations. 13 pages · up to L4
• Reference Lookup material generated from the code — case schema, command line, REST routes, agent tools — plus glossary, bibliography and the authoring guide for this site. 8 pages · up to L4

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