Notes on CFD: General Principles - Symbols

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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

$\text{[math]}$ , $\text{[math]}$

scalars

$\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$

vectors

$\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$

tensors

$\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$

Cartesian axis directions

$\text{[math]}$

identity tensor

$\text{[math]}$

general parameter: scalar, vector or tensor

Geometry and mesh

$\text{[math]}$

cell centre

$\text{[math]}$

face centre

$\text{[math]}$

normal vector of unit length

$\text{[math]}$

point location

$\text{[math]}$

surface

$\text{[math]}$

volume

Numerical methods

$\text{[math]}$

matrix of a matrix equation $\text{[math]}$

$\text{[math]}$

matrix of a matrix equation $\text{[math]}$

$\text{[math]}$

matrix coeﬃcients for row $\text{[math]}$ and column $\text{[math]}$

$\text{[math]}$

source vector of a matrix equation

$\text{[math]}$

source vector of a matrix equation, see above

$\text{[math]}$

scalar coeﬃcent

$\text{[math]}$

internal transformation tensor

$\text{[math]}$

delta coeﬃcient = $\text{[math]}$

$\text{[math]}$

distance from owner cell centre to face centre

$\text{[math]}$

distance from face centre to neighbour cell centre

$\text{[math]}$

skewness vector

$\text{[math]}$

numerical function

$\text{[math]}$

preconditioning matrix

$\text{[math]}$

unit normal vector at face

$\text{[math]}$

conjugate gradient search direction

$\text{[math]}$

ratio of consecutive gradients

single-valued residual

$\text{[math]}$

absolute tolerance

$\text{[math]}$

relative tolerance

$\text{[math]}$

residual vector

$\text{[math]}$

face area vector

$\text{[math]}$

transformation tensor

$\text{[math]}$

rotational tensor

$\text{[math]}$

value fraction

$\text{[math]}$

face weights

$\text{[math]}$

value fraction tensor

$\text{[math]}$

under-relaxation factor

conjugate gradient search magnitude

GAMG correction

$\text{[math]}$

advection limiter

$\text{[math]}$

diﬀusivity

$\text{[math]}$

internal coeﬃcient factor

$\text{[math]}$

centre-to-centre vector

$\text{[math]}$

time step interval

$\text{[math]}$

solution error

$\text{[math]}$

volumetric or mass ﬂux at faces

$\text{[math]}$

negative (incoming) ﬂuxes at faces

$\text{[math]}$

positive (outgoing) ﬂuxes at faces

$\text{[math]}$

Crank-Nicolson oﬀset coeﬃcient

Subscripts

$\text{[math]}$

boundary value/gradient

$\text{[math]}$

downwind interpolation

$\text{[math]}$

exact solution

$\text{[math]}$

values at faces

$\text{[math]}$

high bound value

$\text{[math]}$

linear interpolation

low bound value

$\text{[math]}$

neighbour cell

$\text{[math]}$

owner, or current, cell

$\text{[math]}$

upwind interpolation

Superscripts

$\text{[math]}$

current stored value

$\text{[math]}$

new value

$\text{[math]}$

old time level

$\text{[math]}$

old-old time level

Dimensionless numbers

$\text{[math]}$

Courant number $\text{[math]}$

$\text{[math]}$

Péclet number $\text{[math]}$

Physical quantities (with SI units)

$\text{[math]}$

body force per unit mass $\text{[math]}$

$\text{[math]}$

speed of sound $\text{[math]}$

$\text{[math]}$

speciﬁc heat capacity at constant volume $\text{[math]}$

$\text{[math]}$

mass diﬀusivity $\text{[math]}$

$\text{[math]}$

rate of deformation tensor $\text{[math]}$

$\text{[math]}$

speciﬁc internal energy $\text{[math]}$

$\text{[math]}$

force vector $\text{[math]}$

$\text{[math]}$

gravitational acceleration $\text{[math]}$

$\text{[math]}$

heat transfer coeﬃcient $\text{[math]}$

$\text{[math]}$

heat of formation per unit mass $\text{[math]}$

$\text{[math]}$

turbulent kinetic energy per unit mass $\text{[math]}$

wave number $\text{[math]}$

$\text{[math]}$

speciﬁc kinetic energy $\text{[math]}$

$\text{[math]}$

characteristic length $\text{[math]}$

$\text{[math]}$

turbulent mixing length

$\text{[math]}$

molar mass $\text{[math]}$

$\text{[math]}$

heat per unit surface area $\text{[math]}$

$\text{[math]}$

pressure $\text{[math]}$

kinematic pressure $\text{[math]}$

$\text{[math]}$

characteristic pressure

$\text{[math]}$

heat source per unit mass $\text{[math]}$

thermal source $\text{[math]}$

$\text{[math]}$

speciﬁc gas constant $\text{[math]}$

$\text{[math]}$

Universal Gas Constant $\text{[math]}$

$\text{[math]}$

temperature $\text{[math]}$

$\text{[math]}$

standard temperature $\text{[math]}$

$\text{[math]}$

time $\text{[math]}$

$\text{[math]}$

characteristic time

$\text{[math]}$

traction force per unit area $\text{[math]}$

$\text{[math]}$

velocity vector $\text{[math]}$

$\text{[math]}$

velocity in $\text{[math]}$ -direction

$\text{[math]}$

freestream or far-ﬁeld velocity

$\text{[math]}$

characteristic speed

$\text{[math]}$

characteristic speed

$\text{[math]}$

Kolmogorov velocity scale

$\text{[math]}$

turbulent velocity ﬂuctuations

$\text{[math]}$

particle velocity

$\text{[math]}$

mean particle velocity

$\text{[math]}$

spin tensor $\text{[math]}$

$\text{[math]}$

particle position $\text{[math]}$

$\text{[math]}$

thermal diﬀusivity $\text{[math]}$ $\text{[math]}$

$\text{[math]}$

energy diﬀusivity $\text{[math]}$ $\text{[math]}$

$\text{[math]}$

ratio of speciﬁc heat capacities $\text{[math]}$

$\text{[math]}$

boundary layer thickness $\text{[math]}$

$\text{[math]}$

Kolmogorov length scale $\text{[math]}$

$\text{[math]}$

turbulent dissipation rate $\text{[math]}$

$\text{[math]}$

thermal conductivity $\text{[math]}$

Kármán’s constant $\text{[math]}$

$\text{[math]}$

turbulent thermal conductivity

$\text{[math]}$

eﬀective thermal conductivity $\text{[math]}$

$\text{[math]}$

mean free path $\text{[math]}$

$\text{[math]}$

dynamic viscosity $\text{[math]}$

$\text{[math]}$

kinematic viscosity $\text{[math]}$

$\text{[math]}$

(kinematic) turbulent viscosity

$\text{[math]}$

(kinematic) eﬀective viscosity $\text{[math]}$

$\text{[math]}$

(mass) density $\text{[math]}$

$\text{[math]}$

stress tensor $\text{[math]}$

$\text{[math]}$

Reynolds stress

$\text{[math]}$

viscous stress tensor

$\text{[math]}$

turbulent viscous stress tensor

$\text{[math]}$

speciﬁc turbulent dissipation rate $\text{[math]}$

$\text{[math]}$

vorticity $\text{[math]}$

Dimensionless numbers

$\text{[math]}$

Euler number $\text{[math]}$

$\text{[math]}$

Froude number $\text{[math]}$

$\text{[math]}$

Knudsen number $\text{[math]}$

$\text{[math]}$

Mach number $\text{[math]}$

$\text{[math]}$

Péclet number $\text{[math]}$

$\text{[math]}$

Prandtl number $\text{[math]}$

$\text{[math]}$

Reynolds number $\text{[math]}$

$\text{[math]}$

Turbulent Reynolds number $2 = k =$

$\text{[math]}$

Schmidt number $\text{[math]}$

$\text{[math]}$

Strouhal number $\text{[math]}$

Relational symbols

$\text{[math]}$

$\text{[math]}$ and $\text{[math]}$ are equal

$\text{[math]}$

$\text{[math]}$ and $\text{[math]}$ are approximately equal

$\text{[math]}$

$\text{[math]}$ and $\text{[math]}$ are almost exactly equal

$\text{[math]}$

$\text{[math]}$ and $\text{[math]}$ are equivalent

$\text{[math]}$

$\text{[math]}$ is assigned the value of $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ is proportional to $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ is of the order of magnitude of $\text{[math]}$

Notes on CFD: General Principles - Symbols