--- title: What Gyre is summary: Gyre is a differentiable high-order flow solver delivered as a service. It gives a design-optimization framework what it needs from an aerodynamics discipline — converged flows, outputs, coupling fields and exact derivatives — and deliberately nothing more. section: overview order: 1 level: 1 audience: [everyone] keywords: [overview, MDO, differentiable, discipline] --- High-fidelity multidisciplinary design optimization (MDO) couples a flow solver with structures, propulsion, controls and a geometry engine, and drives the whole with a gradient-based optimizer. The flow solver is usually the most expensive and the least cooperative member: its gradients are hard to obtain, hard to trust and hard to keep in sync with the code. **Gyre is a flow discipline designed for that seat.** It is built around three commitments. 1. **Everything is differentiable.** The solver is written in JAX. Jacobian products, adjoints, shape sensitivities and error estimates are produced by automatic differentiation of the same kernels that compute the flow, so they are exact for the discrete problem and can never drift out of sync. 2. **High order, with entropy-conservative volume terms.** A split-form discontinuous Galerkin spectral element method on curved meshes whose volume terms conserve entropy exactly, so aliasing inside an element cannot feed the instability that limits under-resolved high-order methods. A discrete entropy inequality is *proven* with the entropy-stable interface fluxes (`es_roe`, `llf`); with the default classical Roe flux entropy decay is measured, not proven, and positivity is not enforced ([the exact conditions](../theory/two-point-fluxes.md#interface-fluxes)). 3. **A service, not a script.** One deployable unit exposes a REST API, warm analysis sessions for design loops, an agent (MCP) interface, declarative pipelines and this documentation — built from the revision that is running. > **Note: What Gyre is not** > > Gyre contains no optimizer, no design-variable management and no problem formulation. Those > belong to the MDO framework. Gyre's contract ends at: *given inputs, return converged outputs > and exact derivative products*. **[L2 Practice] What you can do with it today** * Solve steady compressible Euler, laminar Navier–Stokes and Reynolds-averaged (Spalart–Allmaras) flows on curved high-order meshes in two and three dimensions: aerofoils, cylinders, channels, flat plates, spheres and ellipsoids from the built-in generators. * Use the built-in mesh generators or bring a mesh of curved quadrilaterals or hexahedra from Gmsh ([mesh files](../guide/meshes.md)). * Obtain lift, drag, side force, moments, heat flux and consistent nodal surface loads. * Obtain total derivatives of any scalar output with respect to Mach number, angle of attack, sideslip, Reynolds number, turbulence-model data and the position of every surface node, by adjoint or direct method. * Couple to another discipline through surface displacements (in) and loads (out), with the forward and reverse products a coupled adjoint needs. * Estimate the discretization error of an output with one extra linear solve, and let the solver raise the polynomial degree until that estimate meets a tolerance. * Run all of this in-process (Python), from the command line, over HTTP from another machine, or from an AI agent through the Model Context Protocol. **[L2 Practice] A thirty-second example** ```bash gyre run naca0012_euler --gradients --of cl,cd --wrt alpha,mach --error cd ``` solves inviscid flow over a NACA 0012 at Mach 0.5 and 2°, and prints the force coefficients, their adjoint derivatives with respect to angle of attack and Mach number, and an adjoint-based estimate of how much of the (physically zero) drag is discretization error. The [worked example](../examples/naca0012-euler.md) shows the numbers. **Flow field: Mach number, NACA 0012, M = 0.5, α = 2°.** Interactive viewer in the HTML page (initially showing `mach`). Part of the domain: window x ∈ [-1, 2.5], y ∈ [-1.5, 1.5] · the 354 mesh elements that reach into it · 8×8 points each. Sampled solution (coordinates and fields, base64 float32): [field.json](../data/fields/example_airfoil/field.json). | Field | Minimum in the sample | Maximum in the sample | |---|---|---| | mach | 0.0515553 | 0.716734 | | pressure | 2.39749 | 3.38853 | | density | 0.882255 | 1.12959 | | entropy | 2.84589 | 2.88839 | Provenance: gyre 0.4.0; revision `39979fcf90` (commit `39979fcf902ad6116eb550b881b4278d4599c8e2`); 2026-11-12T11:35:15-0500; device gpu · NVIDIA GeForce RTX 3060 Ti; source `example_airfoil/field.json`. **Revision check: Same code as this build.** Produced by 39979fcf902ad6116eb550b881b4278d4599c8e2. Every commit between it and the commit this site was built from (ceb1f4b0bed41de53e586df10858079f5a2bcdd8) changes only documentation text, evidence records or bookkeeping: the code is the same. **[L3 Mechanics] How the pieces relate** | You are… | You interact with… | Start at | |---|---|---| | integrating Gyre into an MDO framework | `FlowDiscipline` / `RemoteDiscipline`, OpenMDAO adapter | [MDO integration](../guide/mdo-integration.md) | | running analyses | CLI, REST jobs | [Getting started](../guide/getting-started.md) | | an AI agent or building one | MCP tools | [Agent interface](../guide/agents.md) | | operating a deployment | `tools/deploy.py`, container, metrics | [Deployment](../guide/deployment.md) | | extending the solver | `gyre.dg`, `gyre.physics`, `gyre.implicit` | [Code structure](../engineering/code-structure.md) | | assessing the numerics | verification studies | [Verification](../verification/index.md) | **[L3 Mechanics] Design principles** * **One execution path.** CLI, service workers, sessions, pipelines and agent tools all call the same `run_case` / `FlowDiscipline` code. There is no second implementation to diverge. * **Geometry is data.** Node coordinates are an argument of the differentiated function, not configuration, so shape derivatives need no dedicated code. * **Matrix-free everywhere.** Jacobians are applied, never stored; preconditioner blocks come from AD as well. * **Evidence travels with the code.** Verification numbers shown in these pages are files produced by `gyre verify` and stamped with commit, device and time. * **Honest scope.** Limits are stated where they apply ([capabilities and limits](capabilities-and-limits.md)).