# Progress in Numerical Modelling: The Finite Difference Method

• Marcello Benedini
• George Tsakiris
Chapter
Part of the Water Science and Technology Library book series (WSTL, volume 70)

## Abstract

Some partial differential equations (PDE) that describe several hydrodynamic phenomena do not have analytical solution, and hence they can only be solved by numerical methods. The finite difference method (FDM) is traditionally the most efficient way for numerical integration of PDEs, now empowered by the availability of computing facilities. Applied to the water quality models, the FDM has been developed according to several numerical schemes which are useful in practical applications. Some of these numerical schemes are described in this chapter, focussing on their particular characteristics, in order to provide guidance for the most frequently encountered cases of pollution in rivers and streams.

## Keywords

Numerical Scheme Finite Difference Method Pollutant Concentration Finite Difference Method Pollution Transport
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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