---
title: Glossary
summary: Short definitions of the terms used across this documentation, with pointers to where each is explained.
section: reference
order: 5
level: 1
keywords: [glossary, terms, definitions]
---
<!-- gyre docs: expanded Markdown of reference/glossary.md (generated tables, verification numbers and chart data are written out). Base level of this page: L1 Essentials; passages at another level are bracketed by 'begin level N' / 'end level N' comments and start with [LN Name]. Built from revision ceb1f4b0be. -->

| Term | Meaning |
|---|---|
| **`x_surface` / `f_surface`** | Surface-node displacements (input) and consistent nodal loads (output): the coupling fields. |
| **Adjoint (discrete)** | Solution $\boldsymbol\psi$ of the transposed linearised residual equation with an output's state derivative as right-hand side; yields derivatives with respect to all inputs at once. [Theory](../theory/adjoint-and-sensitivities.md) |
| **Adjoint consistency** | Property that the discrete adjoint is a consistent discretization of the continuous adjoint problem; enables superconvergent outputs and sharp error estimates. |
| **Block Jacobi** | Preconditioner that inverts the element-diagonal blocks of the Jacobian. |
| **BR2** | Second Bassi–Rebay scheme for viscous terms: local gradient plus face liftings, compact stencil. [Theory](../theory/viscous-br2.md) |
| **Case specification** | The document (`CaseSpec`) describing mesh, flow, discretization and solver. [Guide](../guide/cases.md) |
| **Checkpoint** | A saved point of a discipline or session (inputs and state) from which it can be restored or rebuilt. [Guide](../guide/mdo-integration.md) |
| **Cubed sphere** | Mesh topology of six blocks, one per face of a cube, projected onto a sphere; three blocks meet at each corner, so it is unstructured. [Example](../examples/sphere.md) |
| **Deployment** | A running service instance together with the documentation built from its revision. |
| **DGSEM** | Discontinuous Galerkin spectral element method: nodal DG on tensor-product Gauss-type points. [Theory](../theory/dgsem.md) |
| **Direct method** | Derivative computation by one linearised solve per input. |
| **Discipline** | In MDO, one analysis (here: the flow solver) exposing inputs, outputs and derivatives. [Guide](../guide/mdo-integration.md) |
| **Eddy viscosity** | Viscosity $\mu_t$ that a turbulence closure adds to the molecular viscosity seen by the mean flow. [Theory](../theory/turbulence-model.md) |
| **Effectivity** | Ratio of an estimated to an actual error (one is ideal). |
| **Entropy conservative / stable** | A scheme whose discrete entropy is conserved / cannot grow, mirroring the continuous equations. |
| **Entropy-stable flux** | Interface flux that produces no entropy for any pair of states; in Gyre `es_roe` (matrix dissipation in entropy variables) and `llf`. [Theory](../theory/two-point-fluxes.md) |
| **FGMRES** | Flexible GMRES: Krylov method tolerating a preconditioner that changes between iterations. |
| **Flux differencing** | Writing volume terms as differences of symmetric two-point fluxes. |
| **Free-stream preservation** | A uniform flow remains exactly uniform on a curved mesh. |
| **JIT** | Just-in-time compilation of traced JAX functions by XLA. |
| **JVP / VJP** | Jacobian–vector / vector–Jacobian product (forward / reverse mode AD). |
| **Law of the wall** | Universal velocity profile of a turbulent boundary layer in wall units: $u^+ = y^+$ in the sublayer, logarithmic further out. [Example](../examples/turbulent-flat-plate.md) |
| **LGL** | Legendre–Gauss–Lobatto points: quadrature nodes that include the interval end points. |
| **Lifting** | Mapping of face jumps into an element-wise gradient correction. |
| **Line smoother** | Smoother that solves the block-tridiagonal system of each line of strongly coupled elements exactly; for the thin cells of a wall-resolved mesh. |
| **Mixed precision** | Using single precision for a part of a computation that need not be exact; here the stored blocks of the smoother, while residual, Jacobian products and Krylov vectors stay double. |
| **Matrix-free** | Applying a linear map without storing its matrix; here the Jacobian (always) and the mesh deformation (above a size limit). |
| **MCP** | Model Context Protocol: standard through which AI agents call tools. [Guide](../guide/agents.md) |
| **MDO** | Multidisciplinary design optimization. |
| **Mesh store** | The directory of a deployment that holds uploaded mesh files; a case refers to a stored mesh by its name. [Guide](../guide/meshes.md#meshes-in-a-service) |
| **MMS** | Method of manufactured solutions: forcing the equations so that a chosen function is the exact solution. |
| **Order selection** | Raising the polynomial degree of a case until the adjoint-based error estimate of one output meets a tolerance (`adapt`, `--target-error`). |
| **p-multigrid** | Multigrid over polynomial degrees on a fixed mesh. |
| **Physical group** | In Gmsh, a named set of curves or surfaces; the physical groups of the boundary become the boundary groups of an imported mesh. [Guide](../guide/meshes.md#boundary-groups-and-conditions) |
| **Provenance** | Revision, device and time attached to a result. |
| **PTC** | Pseudo-transient continuation: globalised Newton iteration with an artificial time step. |
| **RANS** | Reynolds-averaged Navier–Stokes equations: the mean flow of a turbulent flow, closed by a turbulence model. [Theory](../theory/turbulence-model.md) |
| **SA-neg** | The Spalart–Allmaras one-equation turbulence model in its negative form, which stays well posed when $\tilde\nu$ undershoots below zero. [Theory](../theory/turbulence-model.md) |
| **SBP** | Summation by parts: discrete integration by parts. |
| **Session** | A long-lived solver process in the service for repeated evaluations. |
| **Sideslip** | Angle $\beta$ between the free stream and the $x$–$y$ plane in 3-D; input `beta`. [Theory](../theory/outputs-and-functionals.md) |
| **Split-argument residual** | Residual taking the state in "own" and "neighbour" roles; its own-derivative is block diagonal. |
| **Tailnet** | A private network of devices (Tailscale); Gyre services bind to all interfaces to be reachable on it. |
| **Total derivative** | Derivative of an output including the implicit dependence through the converged state. |
| **Two-point flux** | Symmetric numerical flux of two states used inside elements. [Theory](../theory/two-point-fluxes.md) |
| **Wall distance** | Distance $d$ to the nearest no-slip wall, an input of the turbulence model; computed to the curved wall and differentiated with the geometry. [Theory](../theory/turbulence-model.md) |
| **Wall units** | Lengths and velocities scaled with the friction velocity and the viscosity: $y^+$, $u^+$. |
| **Weak-form residual** | Residual scaled by the diagonal mass matrix, $\mathbf R_w = (wJ)\mathbf R$. |