Script > Ch 7
7: Environmental quality modeling
Until now we have derived governing equations for and sought
solutions to idealized cases where analytical solutions could be found.
Many problems in the natural world, however, are complex enough that simplified analytical solutions are inadequate to
predict the transport and mixing behavior. In these situations,
approximations of the governing transport equations (such as finite difference) must be made
so that numerical solutions can be found. These approximations can be simple or complex, but
often result in a large number of equations that must be solved to predict the concentration distribution.
Hence, computer algorithms are used to make the numerical solutions tractable.
In this chapter, we introduce the field of
environmental quality modeling
based on computerized (numerical or digital) tools. This
chapter begins by outlining how to select an appropriate numerical tool.
Next, we describe common computer approximations. First, simple numerical models based on plug-flow and
continuously-stirred tank reactors are introduced. Second, an
overview of numerical approximations to the governing equations is presented.
Because we are now dealing with approximate solutions, new procedures are needed to assure that our results
are acceptable. The final section outlines the crucial steps
necessary to test the accuracy of a numerical result. Although
computer power is rapidly growing, it remains important to use simple tools and thorough testing in order to understand and
synthesize the meaning of numerical results.