Page 218 - Finite Element Analysis with ANSYS Workbench

11.1 Basic Equations 209

11.1.2 Solution Approach

By observing the three differential equations above, the
velocity components u and v should be determined from the x- and
y-momentum equations. This means the pressure p should be
obtained from the mass equation. However, the mass equation
does not contain the pressure p at all. Thus, the pressure p must be
determined together with the velocity components u and v in the
momentum equations such that the mass is also satisfied.
The idea above suggests that the solution process
should be an iteration process. The process is continued until the
converged solutions of u, v and p are achieved.
It is noted that the x- and y-momentum equations

contain the convection terms which are in form of the first-order
partial derivative. These convective terms are nonlinear and
require additional effort for solutions. These terms may yield
oscillated solutions if the mesh is not fine enough. Fine mesh is
thus normally needed which requires more computational time.
These factors must be realized prior to solving flow problems using
any CFD software.

11.2 Finite Volume Method

The finite volume method is a popular method for
analyzing CFD problems. The method provides accurate flow
solution with reasonable computational effort. Details of the
method can be found in many CFD textbooks including the one
written by the author.
The method starts from dividing the computational
domain into a number of cells as shown in the figure. Herein, we
use rectangular cells to simplify explanation of the method. Each
cell consists of the three unknowns which are the velocity
components u, v and the pressure p. The cell is surrounded by the
north cell N, the east cell E, the south cell S, and the west cell W.
The concept of staggered grids is applied to reduce error that might
occur during the computation.