1. Introduction & Methodology
The equation of momentum in the x and y directions is discretized using the finite volume method and has the following general form:
(1)
\[
a_P \phi_P = \sum a_{NB} \phi_{NB} + S
\]
The continuity equation is converted into a pressure correction equation using the SIMPLE algorithm. The final discrete equation is written in the form of equation (1).
For the discretization of variables on the control volume surfaces, the upstream difference approach and the power-law method are applied.
The governing equations, which are Navier-Stokes, are defined in the following two-dimensional form:
(2)
\[
\frac{\partial (\rho u)}{\partial x} + \frac{\partial (\rho v)}{\partial y} = 0
\]
(3)
\[
\frac{\partial (\rho u u)}{\partial x} + \frac{\partial (\rho v u)}{\partial y} = -\frac{\partial p}{\partial x} + \frac{\partial}{\partial x} \left( \mu \frac{\partial u}{\partial x} \right) + \frac{\partial}{\partial y} \left( \mu \frac{\partial u}{\partial y} \right)
\]
(4)
\[
\frac{\partial (\rho u v)}{\partial x} + \frac{\partial (\rho v v)}{\partial y} = -\frac{\partial p}{\partial y} + \frac{\partial}{\partial x} \left( \mu \frac{\partial v}{\partial x} \right) + \frac{\partial}{\partial y} \left( \mu \frac{\partial v}{\partial y} \right)
\]
