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The system of governing equations for a single-component fluid, written to describe the mean flow properties, is cast in integral
Cartesian form for an arbitrary control volume
with differential surface area
as follows:
where the vectors
, and
are defined as
and the vector
contains source terms such as body forces and energy sources.
Here
,
,
, and
are the density, velocity, total energy per unit mass, and pressure of the fluid, respectively.
is the viscous stress tensor, and
is the heat flux.
Total energy
is related to the total enthalpy
by
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(18.5-2) |
where
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(18.5-3) |
The Navier-Stokes equations as expressed in Equation
18.5-1 become (numerically) very stiff at low Mach number due to the disparity between the fluid velocity
and the acoustic speed
(speed of sound). This is also true for incompressible flows, regardless of the fluid velocity, because acoustic waves travel infinitely fast in an incompressible fluid (speed of sound is infinite). The numerical stiffness of the equations under these conditions results in poor convergence rates. This difficulty is overcome in
ANSYS FLUENT's density-based solver by employing a technique called (time-derivative) preconditioning [
372].