# The modelling system HDWAM

The Aquantec GmbH has redeveloped the hydro-dynamic wave-propagation model HDWAM (HydroDynamisches WellenAblaufModell) specifically to assess and manage flood riscs (Krauter 2002). Even complex water management situations can easily and efficiently be modelled with HDWAM.
Currently, HDWAM solves a simplified version of the St. Vernant equations, which does result in a large speed advantage for simulations of all sizes. We are in the process of developing a solver for the complete equation, which allows for more dependable solutions and simpler models for more complex flow regiems.
HDWAM and its predecessor WSPINI has so far been sucessfully utilized in the production of flood risc maps in the Upper Rhine valley, an operational flooding-after-dyke-break model (Homagk 2009) in the same area as well as operational water level and discharge forecasting between Karlsruhe and Cologne.
The system provides analysis programs, which range from assessing simulation quality, ‘standard’ display of results as time series to GIS-based maps of water speed and depth.

## General structure

Each HDWAM-model consistets of a combination of three different element-base-types:

• surface areas are represented by reservoir-elements
• connections, which link different reservoir-elements
• boundary conditions

In the solver, the partial differential equations for the reservoir-elements are locally discreetised according to a finite-volumina-method and, concurrently, with a 1-step, implizit schema. When combined with connections and boundary conditions, this forms a non-linear system of equations representing the discharge and water levels at each time-step. Utilizing linearisation, this system ist solved iteratively according to a stabilized biconjugated-gradients method.

### Reservoirs

To represent the local topography and structure, one can choose between three reservoir-type elements:

With caskets, one can represent areas where the local water level behaviour is a secondary consideration. While the volume over the area is exact, it approximates the water level horizontally.

#### 1D-riverbeds

Areas, where one can expect a flow mainly moving in on direction, e.g. the main bed of the river, are modelled as 1D-riverbeds.

#### 2D-areas

Large variability in flow directions are modelled as 2D-areas. A good example is flooding as a results of a dyke-break.

### Connections

HDWAM offers the following elements to connect the different reservoir-elements:

#### General hydraulic structures

Buildings like bridges, pipes, specific weirs, etc can be added as a spreadsheet, which translates the waterlevel or discharge on one side to a discharge or waterlevel on the other side. Actively controlled structures can be simulated via a ‘degree-of-opening’ for each structure and/or constrained flow direction.

Special types of hydraulic buildings are as follows:

#### Weir control

Can be used to simulated weirs which are adjusted according to waterlevel and/or discharge.

#### Breaches

Used to represent breakes in dykes and similar structures. This includes a configurable start date as well as width and depth.

#### Dams

Are used to simulate the overflow of large and wide topographic structures like dams, roads and similar.

#### Q-H- or H-Q-Connections

Are used to enforce discharge and water level continuity between two elements.

### Boundary conditions

It is possible to set hydrological time series, both discharge and water level, as model input- and output conditions. It is also possible to set a discharge curve as an output-condition.