# 1D Hydrodynamic models

## Fundamentals of mathematical river modelling

A solid understanding of the underlying mathematics is needed in order to be able to judge the adequacy of a mathematical method and its application limits. This knowledge helps to analyse how precisely the flow is described mathematically, which simplifying assumptions were made, and how they affect the result of the calculation. To help satisfying this need, the theoretical foundations of the two most common fundamental model approaches in engineering practise, the one-dimensional water level model and the two-dimensional shallow water model, will be discussed in detail in the following chapters.

## One-dimensional water level calculation

Intention:

• calculation of the flow situation in watercourses
• the easiest mathematical method for calculating the flow situation in rivers is the water level calculation.

Solution:

• reducing the multi-dimensional real-world flow processes to a one-dimensional problem
• assuming the flow cross-section and the flow velocity at a certain water level or, depending on the used approach, parts of the cross-section to be constant.
• the complex flow situation in the river is thus condensed to be a simple one-dimensional stream tube.