Numerical Methods and Its Solution - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 216

the results are strongly affected by the density of the mesh and distribution of the
grid nodal points.
Round-off error These errors exist due to the difference between the machine ac-
curacy of a computer and the true value of a variable. Every computer represents
numbers that have a finite number of significant figures. The default value of the
number of significant digits for many computers is 7 and this is commonly referred
to as single precision . However, calculations can also be performed using 15 signif-
icant figures, which is referred as double precision . The error due to the retaining of
a limited number of computer digits available for storage of a given physical value
is therefore called the round-off error. This error is naturally random and there is no
easy way of predicting it. It depends on the number of calculations, rounding off
method, rounding-off type, and even sequence of calculations.
Iteration or Convergence error These errors occur due to the difference between
a fully converged solution of a finite number of grid points and a solution that has
not fully achieved convergence. The majority of commercial CFD codes solve the
discretised equations iteratively for steady state solution methodologies. For proce-
dures requiring an accurate intermediate solution at a given time step, this is solved
iteratively in transient methods. It is expected that progressively better estimates of
the solution are generated as the iteration step proceeds and ideally satisfies the im-
posed boundary conditions and equations in each local grid cell and globally over
the whole domain. However, if the iterative process is terminated prematurely then
errors arise. Convergence errors therefore can occur because of either being impa-
tient to allow the solution algorithm to complete its progress to the final converged
solution or applying too large convergence tolerances to halt the iteration process
when the CFD solution may still be considerably far from its converged state.
Physical modeling error These errors are those due to uncertainty in the formulation
of the mathematical models and deliberate simplifications of the models. Here, we
reinforce the definition of uncertainty from above where the Navier-Stokes equations
can be considered to be exact and solving them is impossible for most flows of
engineering interest because of lack of sufficient knowledge to model them. The
sources of uncertainty in physical models are:
• the phenomenon is not thoroughly understood,
• parameters employed in the model are known to possess some degree of
uncertainty,
• appropriate models are simplified thus uncertainty is introduced, and
• experimental confirmation of the models is not possible or is incomplete.
Human error There are essentially two categories of errors associated with human
error. Firstly, computer programming errors involve human mistakes made in pro-
gramming, which are the direct responsibility of the programmers. These errors can
be removed by systematically performing verification studies of subprograms of the
computer code and the entire code, reviewing the details inserted into the code, and
performing validation studies of the code. Secondly, usage errors are also due to
application of the code in a less-than-accurate or improper manner. Inexperience in