Glossary · Gyre

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
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
Case specification	The document (`CaseSpec`) describing mesh, flow, discretization and solver. Guide
Checkpoint	A saved point of a discipline or session (inputs and state) from which it can be restored or rebuilt. Guide
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
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
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
Eddy viscosity	Viscosity $\mu_t$ that a turbulence closure adds to the molecular viscosity seen by the mean flow. Theory
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
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
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
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
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
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
SA-neg	The Spalart–Allmaras one-equation turbulence model in its negative form, which stays well posed when $\tilde\nu$ undershoots below zero. Theory
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
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
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
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, $\mathbf R_w = (wJ)\mathbf R$ .