General variables

eqn, eqn    scalars

eqn, eqn, eqn vectors

eqn, eqn, eqn tensors

eqn, eqn, eqn Cartesian axis directions

eqn identity tensor

eqn general parameter: scalar, vector or tensor

Geometry and mesh

eqn    cell centre

eqn face centre

eqn normal vector of unit length

eqn point location

eqn surface

eqn volume

Numerical methods

eqn   matrix of a matrix equation eqn

eqn matrix of a matrix equation eqn

eqn matrix coefficients for row eqn and column eqn

eqn source vector of a matrix equation

eqn source vector of a matrix equation, see above

eqn scalar coefficent

eqn internal transformation tensor

eqn delta coefficient = eqn

eqn distance from owner cell centre to face centre

eqn distance from face centre to neighbour cell centre

eqn skewness vector

eqn numerical function

eqn preconditioning matrix

eqn unit normal vector at face

eqn conjugate gradient search direction

eqn ratio of consecutive gradients

single-valued residual

eqn absolute tolerance

eqn relative tolerance

eqn residual vector

eqn face area vector

eqn transformation tensor

eqn rotational tensor

eqn value fraction

eqn face weights

eqn value fraction tensor

eqn under-relaxation factor

conjugate gradient search magnitude

GAMG correction

eqn advection limiter

eqn diffusivity

eqn internal coefficient factor

eqn centre-to-centre vector

eqn time step interval

eqn solution error

eqn volumetric or mass flux at faces

eqn negative (incoming) fluxes at faces

eqn positive (outgoing) fluxes at faces

eqn Crank-Nicolson offset coefficient


eqn    boundary value/gradient

eqn downwind interpolation

eqn exact solution

eqn values at faces

eqn high bound value

eqn linear interpolation

low bound value

eqn neighbour cell

eqn owner, or current, cell

eqn upwind interpolation


eqn    current stored value

eqn new value

eqn old time level

eqn old-old time level

Dimensionless numbers

eqn   Courant number eqn

eqn Péclet number eqn

Physical quantities (with SI units)

eqn    body force per unit mass eqn

eqn speed of sound eqn

eqn specific heat capacity at constant volume eqn

eqn mass diffusivity eqn

eqn rate of deformation tensor eqn

eqn specific internal energy eqn

eqn force vector eqn

eqn gravitational acceleration eqn

eqn heat transfer coefficient eqn

eqn heat of formation per unit mass eqn

eqn turbulent kinetic energy per unit mass eqn

wave number eqn

eqn specific kinetic energy eqn

eqn characteristic length eqn

eqn turbulent mixing length

eqn molar mass eqn

eqn heat per unit surface area eqn

eqn pressure eqn

kinematic pressure eqn

eqn characteristic pressure

eqn heat source per unit mass eqn

thermal source eqn

eqn specific gas constant eqn

eqn Universal Gas Constant eqn

eqn temperature eqn

eqn standard temperature eqn

eqn time eqn

eqn characteristic time

eqn traction force per unit area eqn

eqn velocity vector eqn

eqn velocity in eqn-direction

eqn freestream or far-field velocity

eqn characteristic speed

eqn characteristic speed

eqn Kolmogorov velocity scale

eqn turbulent velocity fluctuations

eqn particle velocity

eqn mean particle velocity

eqn spin tensor eqn

eqn particle position eqn

eqn thermal diffusivity eqn eqn

eqn energy diffusivity eqn eqn

eqn ratio of specific heat capacities eqn

eqn boundary layer thickness eqn

eqn Kolmogorov length scale eqn

turbulent dissipation rate eqn

eqn thermal conductivity eqn

Kármán’s constant eqn

eqn turbulent thermal conductivity

eqn effective thermal conductivity eqn

eqn mean free path eqn

eqn dynamic viscosity eqn

eqn kinematic viscosity eqn

eqn (kinematic) turbulent viscosity

eqn (kinematic) effective viscosity eqn

eqn (mass) density eqn

eqn stress tensor eqn

eqn Reynolds stress

eqn viscous stress tensor

eqn turbulent viscous stress tensor

eqn specific turbulent dissipation rate eqn

eqn vorticity eqn

Dimensionless numbers

eqn   Euler number eqn

eqn Froude number eqn

eqn Knudsen number eqn

eqn Mach number eqn

eqn Péclet number eqn

eqn Prandtl number eqn

eqn Reynolds number eqn

eqn Turbulent Reynolds number  2 = k =

eqn Schmidt number eqn

eqn Strouhal number eqn

Relational symbols

eqn    eqn and eqn are equal

eqn eqn and eqn are approximately equal

eqn eqn and eqn are almost exactly equal

eqn eqn and eqn are equivalent

eqn eqn is assigned the value of eqn

eqn eqn is proportional to eqn

eqn eqn is of the order of magnitude of eqn

Notes on CFD: General Principles - Symbols