Glossary

Accuracy

A measure of the similarity of a simulation to the physical flow it is intended to represent. See also Numerical accuracy.

Adaptive grid refinement

Adaptive grid refinement Refinement of a computational grid based, for example, on regions with steep flow gradients. This can be an automatic, manual or semi-manual procedure.

Bernoulli equation

Bernoulli equation This refers to an equation that expresses conservation of fluid kinetic energy, gravitational potential energy and energy associated with pressure in the absence of all other energy transfer mechanisms, including viscous dissipation.

Boundary condition

Spatial or temporal specification of variable values or behaviour necessary to produce a unique solution.

Boundary layer

Boundary layer The layer of fluid adjacent to solid surfaces that has been affected, through viscous action, by the presence of the solid surface. There are many mathematical descriptions for the boundary layer’s extent and these are required in many turbulence models. The simplest description is the region, adjacent to a solid surface, where the fluid velocity is less than the free stream velocity (velocity outside the boundary layer) by more than 1 %.

Buffer layer

Buffer layer A region in the turbulent boundary layer linking the viscous sub-layer to the fully turbulent zone.

Cell

Discrete area or volume over which governing equations are integrated. The complete group of cells should define the domain under consideration.

CFD (Computational Fluid Dynamics)

The field of solving complex non-linear differential equations governing fluid flow using computer.

CFL (Courant-Friedrich-Lewy) condition

Courant-Friedrich-Lewy condition The Courant-Friedrich-Lewy condition states that the Courant number should be less than or equal to unity.

Closure

Closure

Generally used in relation to turbulence modeling. For turbulent flows, the governing equations (when the RANS approach is used) have turbulence correlations that need to be accounted for using empirically based models. Such models enable closure of the problem, i.e. give sufficient equations for the number of unknowns, thus enabling a solution to be produced. Examples of closure models include k-ε, RSM etc.

Computational domain

Computational domain

The geometrical region over which a simulation is performed. Sometimes referred to as the analytical domain or computational domain.

Conservation

Conservation

The preservation of an extensive property in a closed system.

Conservation form of equations

Equations written in a form that directly represents the quantity conserved; mass, momentum, energy, rather than velocity and temperature. The equations can then be expressed as: Rate of Change of Conserved Quantity = Diffusion + Convection + Sources - Sinks

Continuity

Continuity

A system that exhibits continuity and expresses conservation (generally of mass).

Control surface

Control surface

The bounding surface of a control volume

Control volume

Control volume

The volume over which the partial differential equations describing fluid flow are integrated to obtain discretized (algebraic) equations.

Convergence

Convergence

Error calculated from summing terms in partially converged equations.

Courant number

Courant number

The speed of sound, multiplied by the ratio of the time step length to the cell length. This ratio is the time required for a quantity or fluid particle to be convected through a small distance. Therefore, the Courant number can be viewed as a time step to convection time scale ratio.

Derivatives

Derivatives

Variables differentiated with respect to either time or space.

Diffusion

Diffusion

The natural movement of species or properties from regions of high concentration to those of lower concentration. Diffusion is modeled mathematically using Fick’s Law.

Discontinuities

Sudden changes in the value of a variable. For example, shock waves.

Discretization

Process by which the governing partial differential equations are converted into algebraic equations associated with discrete elements.

Divergence

The progression of a numerical scheme away from any single answer. The opposite of convergence.

DNS (Direct Numerical Simulation)

A method in which the turbulent flow is directly numerically simulated without any form of time or length averaging, i.e. both the mean flow and all turbulent fluctuations (eddies) are simulated. Since turbulent eddies are both three-dimensional and unsteady (time-variant), simulations using this method must also be both three-dimensional and unsteady and, since the length and time scales of turbulent eddies cover a large range, both the grid size and the time-step size must be very small to account for the smallest fluctuations. This makes this method very computationally expensive and even with current state-of-the-art computer hardware, only practical for simple flows at low Reynolds numbers.

Dynamic boundary condition

Dynamic boundary condition

A boundary condition which changes with time.

Dynamic pressure

Dynamic pressure

Pressure due to local kinetic energy (½ρv2)

Elements

The basic building blocks of the finite element model, which together form the (finite element) grid. In CFD, elements are normally triangular or quadrilateral in 2D and tetrahedra, prisms (wedges), pyramids or hexahedra in 3D.

Equilibrium

A fluid system is said to be in (hydrodynamic) equilibrium when it experiences no net forces or accelerations (the velocity at each point remains constant over time).

FDM (Finite Difference Method)

A method of approximating gradients as part of the procedure for numerical solution of differential equation, by estimating a derivative by the ratio of two finite differences.

FEM (Finite Element Method)

A computational method that originated from structural analysis but which is also applied to CFD, in which the computational domain is subdivided into a finite number of elements over which discretized equations are solved.

FVM (Finite Volume Method)

A computational method in which the computational domain is subdivided into a finite number of control volumes over which discretized governing equations are solved. Primarily used for CFD.

Grid/mesh

The outcome of splitting up the computational domain (discretization) into a number of elements or cells defining the discrete points at which the numerical solution is computed. The points are normally the cell centers or cell vertices.

Grid generation

The act of generating a set of grid points for which the solution will be calculated.

Grid independence

Having run a simulation on a sequence of grids (usually refining each time) and found the same results for each grid, the solution is considered grid-independent. The converged solution is therefore independent of the size of grid (beyond a certain limit) used to obtain the solution.

Hybrid grid

Hybrid grid

A computational grid containing more than one cell or element type.

Incompressible flow

Incompressible flow

Flow where the density is not a function of pressure, i.e. the flow remains at a constant density (less than approximately Mach 0.3) in all locations.

Initial conditions

Conditions at the initial (start) time in a time dependent simulation.

Internal flows

A fluid flow domain that is contained by and passes through a solid structure. All boundaries of the domain can be defined as walls, periodic boundaries, inlets or outlets.

Inviscid flow

Inviscid flow

Flows for which viscosity or shear effects can be ignored. By making this assumption the Euler equations (a subset of the Navier-Stokes equations) can be used, simplifying the solution techniques.

Irrotational flow

Irrotational flow

Flows in which the curl of the velocity is equal to zero. In physical terms, individual elements of fluid have motion described by translation without rotation. By making this assumption along with the inviscid assumption a potential flow problem can be solved.

Iterative method

Iterative method

A process in which the equations are not solved directly but indirectly by a series of iterative steps or iterations. An initial estimate of the solution is made, and an algorithm defined whereby the estimate is improved until it satisfies the equations to within some specified tolerance (see convergence criterion). Linear systems can be solved directly in one step by direct methods. Non-linear systems, typical of CFD problems, will necessarily be iterative.

k-ε turbulence model

A two-equation turbulence model, formulated by the use of the eddy-viscosity hypothesis, where the effect of turbulence is captured by the fluid turbulent kinetic energy (k) and energy dissipation rate (ε).

Laminar flow

Flow in which fluid moves in layers, without turbulence. Diffusive and dissipative effects take place only by molecular diffusion. Laminar flow usually exists at low Reynolds numbers. In practice, for normally encountered flows of low viscosity (air, water), laminar flow only occurs at low velocity or very small physical length scales. However boundary layers can exhibit laminar behavior even at high speeds and on relatively large engineering components, because the dominant length scale is the small thickness of the boundary layer.

Laminar sublayer

In a turbulent boundary layer, the region of fluid closest to the wall where the fluid motion is dominated by viscous effects and turbulent motion is suppressed by viscous action.

LES (Large Eddy Simulation)

LES (Large Eddy Simulation)

This may be considered a compromise between direct numerical simulation (DNS) and the use of turbulence models (RANS). The unsteady flow equations are solved for the mean flow and larger eddies and a ‘sub-grid scale’ model is used to simulate the effects of the smaller eddies. Since it is the largest eddies which contain the most energy and interact most strongly with the mean flow, the LES approach results in a good model of the main effects of the turbulence. Since the grid size no longer has to be small enough to allow for the smallest turbulent eddies, this method is much less computationally expensive than DNS and may be applied to a wider range of flows. However, time dependent simulations using relatively fine meshes are still necessary, so the computational requirement is still high.

Moving mesh

A mesh which is updated with time, in order for moving boundary problems to be analyzed.

Navier-Stokes equations

Navier-Stokes equations

The momentum equations for viscous flow.

Numerical accuracy

A measure of the accuracy of the numerical treatment (i.e. discretization and convergence) and one of the measures by which a solution is verified.

Numerical instability

An increasing oscillation of an iterative solution or the growth of errors due to round-off or truncation in a numerical scheme.

Order of accuracy

The number of terms retained in the series expansion used to approximate the equations in their discretized form.

Outlet boundary condition

Boundary at which fluid leaves the flow domain. Often specified as a constant pressure boundary.

Pathline

An imaginary line which represents the path travelled by an individual particle of fluid. In steady flow, pathlines coincide with streamlines.

Post-processing

Extracting the required data from a completed simulation and presenting it in a readily understood form, often graphically.

Pre-processing

Definition of the flow to be simulated (fluid properties, geometry, mesh generation, boundary conditions, etc.).

RANS (Reynolds-Averaged Navier-Stokes)

RANS (Reynolds-Averaged Navier-Stokes)

A form of the Navier-Stokes equations in which additional terms (known as Reynolds stresses) are included to account for the time averaged effects of turbulence. See Turbulence Models.

Residual

Error calculated from summing terms in partially converged equations.

Reynolds number

A dimensionless number that is the ratio of inertial to viscous forces.

Skewness

A non-dimensional parameter which characterises the extent to which a cell is deformed from an equilateral cell of equivalent volume and the same basic shape (triangle, square, cube, etc.).

Solution adaptive mesh

Solution adaptive mesh

A CFD grid that automatically adjusts to the emerging CFD solution. It has the substantial advantage that steep gradients of dependent variables can be resolved with a locally refined grid, which does not have to be fixed in advance of starting the simulation. Solution adaptive grids are often used in the capture of sharp flow features such as shocks or moving deflagration fronts.

Stability

The property of a numerical method that progresses towards a solution without wild oscillations or divergence.

Steady state flow

a flow field that is independent of time.

Step size

Spatially, the step size is the cell size. Temporally, the step size is the size of the time increments.

Stiff problems

Stiff problems occur when there are two or more very different scales of the independent variables on which the dependent variables are changing.

Streamline

An imaginary instantaneous line, which characterizes a flow such that, at every point along the line, the velocity vector is tangent to the line. For steady flow, streamlines and pathlines are identical.

Strong coupling

Two phenomena are strongly coupled when their dynamics lie within the same order of magnitude. Changes in one system will have a strong influence on the other.

Transient/unsteady flow

Flow which changes with time.

Transitional flow

Flow which changes from exhibiting laminar behavior to turbulent behavior.

Turbulence

A chaotic state of fluid motion where the velocity and pressure change continuously with time.

Turbulence models

Sets of equations that determine the turbulent transport terms in the mean flow equations. They are based on hypotheses about turbulent processes and generally require significant empirical input in the form of constants or functions. These time averaged models do not simulate the details of the turbulent motion (the turbulent eddies), only the effect of turbulence on the mean flow behavior. Thus, with a particular set of empirical constants, they are valid only for a certain flow or at most a range of flows. This is also known as a RANS approach (Reynolds Averaged Navier-Stokes).

Turbulent kinetic energy

The kinetic energy associated with the turbulent fluctuations in velocity.

Two-equation model

A turbulence model that uses two transport equations to model the effects of turbulence on RANS equations (for example, k-ε or k-ω).

Viscosity

Viscosity

The resistance of a fluid to shear; relating shear stress to the rate of angular deformation of fluid elements.

Viscous sub-layer

The region close to a wall in which the viscous forces dominate the flow.

Wall functions

Functions used to describe the effects of turbulent boundary layers in the region adjacent to a wall, without resolving details of the near wall flow and eliminating the need for high grid resolution in the viscous sub-layer.

Weak coupling

Systems are weakly coupled when their dynamics are very different, and changes in one will not have a large influence on the other.

y+

y+

A non-dimensional description of distance from a wall in relation to local flow and wall shear stress parameters. The expression of distances from the wall in y+ ‘units’ is important in defining velocity and turbulence distributions in a universal form suited to wall functions. A very important requirement in the application of wall functions in CFD is that the computational cells adjacent to the wall have a height, usually expressed in y+ units, compatible with the wall functions being employed.

Zero-gradient boundary condition

A boundary condition where a variable is defined as constant across the boundary.