CFD Concepts Quick-Recall Vocabulary

A comprehensive set of vocabulary flashcards covering the core concepts, mathematical models, numerical schemes, and verification techniques found in a Computational Fluid Dynamics (CFD) methods course.

Potential Flow

An inviscid and irrotational model that cannot capture viscosity, boundary layers, separation, or strong shocks; it is trustworthy only for attached, thin-boundary-layer, low-disturbance flow.

Euler Equations

Governing equations that capture rotationality, true compressible convection, and shocks (with correct jump conditions) but miss viscosity and heat conduction.

Navier–Stokes Equations

Equations that add viscous stress and heat conduction to the Euler model, enabling the simulation of boundary layers, separation, and skin friction.

RANS, LES, and DNS

Categories of turbulence treatment within the Navier–Stokes framework: RANS averages, LES spatially filters and models subgrid scales, and DNS resolves every scale.

Equation of State (EOS)

A relation, such as the ideal gas law, that links pressure ($p$), density ($\rho$), and temperature ($T$) to close a compressible system.

Elliptic PDEs

A classification where information travels everywhere and the whole field is coupled; typical of incompressible pressure or subsonic potential flow.

Parabolic PDEs

A classification where information marches forward while diffusing, such as in boundary layers or unsteady diffusion.

Hyperbolic PDEs

A classification where information travels along characteristics at finite speed, typical of Euler equations or supersonic flow.

Conservation (Divergence) Form

A mathematical formulation written as the divergence of fluxes that telescopes discretely to conserve mass, momentum, and energy exactly, providing correct shock speeds.

Characteristics

Curves along which information propagates in hyperbolic systems; they define correct non-reflecting boundary conditions.

Riemann Invariants

Quantities that remain constant along characteristics and underpin Riemann-solver flux methods.

Reynolds Number ($Re$)

A nondimensional number representing the ratio of inertia forces to viscous forces: $\frac{\text{inertia}}{\text{viscous}}$.

Mach Number ($Ma$)

A nondimensional number representing the ratio of flow speed to the local speed of sound: $\frac{\text{speed}}{\text{sound speed}}$.

Prandtl Number ($Pr$)

A nondimensional number representing the ratio of momentum diffusion to thermal diffusion.

Immersed Boundary Method

A strategy where the body is placed inside a non-conforming (often Cartesian) grid; it offers trivial handling of complex geometry but makes near-wall resolution difficult.

Overset (Chimera) Grids

A method using overlapping grids that interpolate data in overlap regions, ideal for components that move relative to each other.

O-grid Topology

A mesh layout where grid lines loop around the body; it is good for blunt bodies but can pinch at sharp trailing edges.

C-grid Topology

A mesh layout that wraps a "C" shape around a body and trails into the wake, commonly used for airfoils.

Adaptive Mesh Refinement (AMR)

A technique for adding resolution dynamically consisting of h-refinement (subdividing cells), p-refinement (raising polynomial order), or r-refinement (relocating nodes).

$$y^{+}$$

The non-dimensional wall-normal distance of the first cell; $y^{+} \approx 1$ indicates wall-resolved resolution, while $y^{+} \approx 30+$ indicates the use of wall functions.

Finite Volume Method (FVM)

The production standard for CFD which integrates conservation laws over control volumes and balances face fluxes to ensure conservation on any cell shape.

Discontinuous Galerkin (DG)

A method using piecewise polynomials that are discontinuous across faces (coupled by fluxes), offering high order and geometric flexibility.

Lattice Boltzmann Method

A mesoscopic method that evolves particle distribution functions on a lattice via streaming and collision, recovering Navier-Stokes in a limit.

Upwind Differencing

A discretization that biases the stencil in the direction of incoming information (flow/characteristic direction) to add numerical dissipation for stability.

Collocated Variable Arrangement

Storing all variables at the same point, which risks pressure checkerboarding unless fixed by methods like Rhie–Chow interpolation.

MUSCL

Monotonic Upstream-centered Scheme for Conservation Laws; it provides slope-limited linear reconstruction for second-order accuracy without oscillations near shocks.

WENO

Weighted Essentially Non-Oscillatory scheme; it blends candidate stencils with smoothness-based weights to provide high order in smooth regions and non-oscillatory capture near shocks.

Roe Scheme

An approximate Riemann solver using a Roe-averaged linearized Jacobian; it is accurate at shocks but requires an entropy fix to avoid non-physical expansion shocks.

HLLC Solver

An HLL-family solver that restores the contact/shear wave (the "C"), allowing it to resolve boundary layers and contacts better than the basic HLL solver.

TVD (Total Variation Diminishing)

A property of schemes that ensures the solution's total variation does not grow, preventing new spurious oscillations near discontinuities.

MacCormack Scheme

An explicit second-order predictor-corrector scheme that uses alternating one-sided differences; it is easy to code for nonlinear conservation laws.

ADI (Alternating Direction Implicit)

A technique that splits a multidimensional implicit solve into sequential 1-D sweeps to maintain stability at a lower computational cost.

Dual (Pseudo-) Time Stepping

A method for unsteady implicit simulations where an inner pseudo-time iteration converges each physical step to maintain time accuracy.

Multigrid

An acceleration technique that moves error to coarser grids where low-frequency error becomes high-frequency and is cheaply removed; includes GMG, AMG, and FAS variants.

Low-Mach Preconditioning

A rescaling (e.g., Turkel or Weiss–Smith) that removes acoustic stiffness in compressible solvers as Mach approaches zero ($Ma \rightarrow 0$).

Artificial Compressibility

Adding a pseudo-time density/pressure term to make incompressible equations hyperbolic so they can be marched to steady state like a compressible solver.

SIMPLE Algorithm

Semi-Implicit Method for Pressure-Linked Equations; a loop that guesses pressure, solves momentum, and then corrects pressure/velocity to satisfy continuity.

Rhie–Chow Interpolation

A face-velocity interpolation used on collocated grids to suppress pressure checkerboarding.

k-̠ SST Model

Menter's Shear Stress Transport model; it blends $k-\omega$ near walls with $k-\epsilon$ in the freestream for accurate external aerodynamics.

Lax Equivalence Theorem

A theorem stating that for a consistent scheme on a well-posed linear problem, stability is both necessary and sufficient for convergence ($\text{consistency} + \text{stability} \Rightarrow \text{convergence}$).

CFL Condition

A stability limit defined as $CFL = \frac{a \Delta t}{\Delta x}$; it requires that the numerical domain of dependence includes the physical domain by limiting the time step.

Numerical Diffusion vs. Dispersion

Dissipation (even-derivative terms) damps amplitudes and smears features, while dispersion (odd-derivative terms) causes phase errors and wiggles.

Verification versus Validation

Verification asks "are we solving the equations right?" (code correctness); Validation asks "are we solving the right equations?" (agreement with experiment).

Richardson Extrapolation

A method using solutions from refined grids to estimate the grid-independent value and the observed order of accuracy.

Method of Manufactured Solutions (MMS)

A verification technique where a chosen analytic solution is substituted into the PDE to derive a source term, then used to test the code's accuracy order.

VOF (Volume of Fluid)

An interface-capturing method that tracks the per-cell phase fraction to simulate free surfaces while conserving mass.

Conjugate Heat Transfer (CHT)

The coupled simulation of heat conduction in solids and convection in adjacent fluids.

Domain Decomposition

Partitioning a mesh across processors where each solves a subdomain and exchanges halo/ghost-cell data via MPI; the basis of parallel CFD.