Environmental Fluid Mechanics 1:
Mass Transfer and Diffusion

Course Script > Ch 7

Chapter 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.

See Lecture 12.




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