Symbols
General
variables
General variables
Geometry and mesh
Geometry and mesh
Numerical methods
Numerical methods
Physical quantities (with SI units)
Physical quantities (with SI units)
Relational symbols
Relational symbols
General variables
Geometry and mesh
Geometry and mesh
Numerical methods
Numerical methods
Physical quantities (with SI units)
Physical quantities (with SI units)
Relational symbols
Relational symbols
General variables
, | scalars |
, , | vectors |
, , | tensors |
, , | Cartesian axis directions |
identity tensor |
general parameter: scalar, vector or tensor |
Geometry and mesh
cell centre |
face centre |
normal vector of unit length |
point location |
surface |
volume |
Numerical methods
matrix of a matrix equation |
matrix of a matrix equation |
matrix coefficients for row and column |
source vector of a matrix equation |
source vector of a matrix equation, see above |
scalar coefficent |
internal transformation tensor |
delta coefficient = |
distance from owner cell centre to face centre |
distance from face centre to neighbour cell centre |
skewness vector |
numerical function |
preconditioning matrix |
unit normal vector at face |
conjugate gradient search direction |
ratio of consecutive gradients |
single-valued residual |
absolute tolerance |
relative tolerance |
residual vector |
face area vector |
transformation tensor |
rotational tensor |
value fraction |
face weights |
value fraction tensor |
under-relaxation factor |
conjugate gradient search magnitude |
GAMG correction |
advection limiter |
diffusivity |
internal coefficient factor |
centre-to-centre vector |
time step interval |
solution error |
volumetric or mass flux at faces |
negative (incoming) fluxes at faces |
positive (outgoing) fluxes at faces |
Crank-Nicolson offset coefficient |
Subscripts
boundary value/gradient |
downwind interpolation |
exact solution |
values at faces |
high bound value |
linear interpolation |
low bound value |
neighbour cell |
owner, or current, cell |
upwind interpolation |
Superscripts
current stored value |
new value |
old time level |
old-old time level |
Dimensionless numbers
Courant number |
Péclet number |
Physical quantities (with SI units)
body force per unit mass |
speed of sound |
specific heat capacity at constant volume |
mass diffusivity |
rate of deformation tensor |
specific internal energy |
force vector |
gravitational acceleration |
heat transfer coefficient |
heat of formation per unit mass |
turbulent kinetic energy per unit mass |
wave number |
specific kinetic energy |
characteristic length |
turbulent mixing length |
molar mass |
heat per unit surface area |
pressure |
kinematic pressure |
characteristic pressure |
heat source per unit mass |
thermal source |
specific gas constant |
Universal Gas Constant |
temperature |
standard temperature |
time |
characteristic time |
traction force per unit area |
velocity vector |
velocity in -direction |
freestream or far-field velocity |
characteristic speed |
characteristic speed |
Kolmogorov velocity scale |
turbulent velocity fluctuations |
particle velocity |
mean particle velocity |
spin tensor |
particle position |
thermal diffusivity |
energy diffusivity |
ratio of specific heat capacities |
boundary layer thickness |
Kolmogorov length scale |
turbulent dissipation rate |
thermal conductivity |
Kármán’s constant |
turbulent thermal conductivity |
effective thermal conductivity |
mean free path |
dynamic viscosity |
kinematic viscosity |
(kinematic) turbulent viscosity |
(kinematic) effective viscosity |
(mass) density |
stress tensor |
Reynolds stress |
viscous stress tensor |
turbulent viscous stress tensor |
specific turbulent dissipation rate |
vorticity |
Dimensionless numbers
Euler number |
Froude number |
Knudsen number |
Mach number |
Péclet number |
Prandtl number |
Reynolds number |
Turbulent Reynolds number |
Schmidt number |
Strouhal number |
Relational symbols
and are equal |
and are approximately equal |
and are almost exactly equal |
and are equivalent |
is assigned the value of |
is proportional to |
is of the order of magnitude of |
Notes on CFD: General Principles - Symbols