2.3 Possibilities and Limitations of Numerical Methods
23
2.2 What is CFD?
As we have seen in Chap. 1, flows and related phenomena can be described by
partial differential (or integro-differential) equations, which cannot be solved
analytically except in special cases. To obtain an approximate solution numerically, we have to use a discretization method which approximates the
differential equations by a system of algebraic equations, which can then
be solved on a computer. The approximations are applied to small domains
in space and/or time so the numerical solution provides results at discrete
locations in space and time. Much as the accuracy of experimental data depends on the quality of the tools used, the accuracy of numerical solutions is
dependent on the quality of discretizations used.
Contained within the broad field of computational fluid dynamics are
activities that cover the range from the automation of well-established engineering design methods t o the use of detailed solutions of the Navier-Stokes
equations as substitutes for experimental research into the nature of complex
flows. At one end, one can purchase design packages for pipe systems that
solve problems in a few seconds or minutes on personal computers or workstations. On the other, there are codes that may require hundreds of hours
on the largest super-computers. The range is as large as the field of fluid
mechanics itself, making it impossible t o cover all of CFD in a single work.
Also, the field is evolving so rapidly that we run the risk of becoming out of
date in a short time.
We shall not deal with automated simple methods in this book. The basis
for them is covered in elementary textbooks and undergraduate courses and
the available program packages are relatively easy to understand and to use.
We shall be concerned with methods designed to solve the equations of
fluid motion in two or three dimensions. These are the methods used in nonstandard applications, by which we mean applications for which solutions (or,
at least, good approximations) cannot be found in textbooks or handbooks.
While these methods have been used in high-technology engineering (for example, aeronautics and astronautics) from the very beginning, they are being
used more frequently in fields of engineering where the geometry is complicated or some important feature (such as the prediction of the concentration
of a pollutant) cannot be dealt with by standard methods. CFD is finding its
way into process, chemical, civil, and environmental engineering. Optimization in these areas can produce large savings in equipment and energy costs
and in reduction of environmental pollution.
2.3 Possibilities and Limitations of Numerical Methods
We have already noted some problems associated with experimental work.
Some of these problems are easily dealt with in CFD. For example, if we want
to simulate the flow around a moving car in a wind tunnel, we need to fix
23
2.2 What is CFD?
As we have seen in Chap. 1, flows and related phenomena can be described by
partial differential (or integro-differential) equations, which cannot be solved
analytically except in special cases. To obtain an approximate solution numerically, we have to use a discretization method which approximates the
differential equations by a system of algebraic equations, which can then
be solved on a computer. The approximations are applied to small domains
in space and/or time so the numerical solution provides results at discrete
locations in space and time. Much as the accuracy of experimental data depends on the quality of the tools used, the accuracy of numerical solutions is
dependent on the quality of discretizations used.
Contained within the broad field of computational fluid dynamics are
activities that cover the range from the automation of well-established engineering design methods t o the use of detailed solutions of the Navier-Stokes
equations as substitutes for experimental research into the nature of complex
flows. At one end, one can purchase design packages for pipe systems that
solve problems in a few seconds or minutes on personal computers or workstations. On the other, there are codes that may require hundreds of hours
on the largest super-computers. The range is as large as the field of fluid
mechanics itself, making it impossible t o cover all of CFD in a single work.
Also, the field is evolving so rapidly that we run the risk of becoming out of
date in a short time.
We shall not deal with automated simple methods in this book. The basis
for them is covered in elementary textbooks and undergraduate courses and
the available program packages are relatively easy to understand and to use.
We shall be concerned with methods designed to solve the equations of
fluid motion in two or three dimensions. These are the methods used in nonstandard applications, by which we mean applications for which solutions (or,
at least, good approximations) cannot be found in textbooks or handbooks.
While these methods have been used in high-technology engineering (for example, aeronautics and astronautics) from the very beginning, they are being
used more frequently in fields of engineering where the geometry is complicated or some important feature (such as the prediction of the concentration
of a pollutant) cannot be dealt with by standard methods. CFD is finding its
way into process, chemical, civil, and environmental engineering. Optimization in these areas can produce large savings in equipment and energy costs
and in reduction of environmental pollution.
2.3 Possibilities and Limitations of Numerical Methods
We have already noted some problems associated with experimental work.
Some of these problems are easily dealt with in CFD. For example, if we want
to simulate the flow around a moving car in a wind tunnel, we need to fix