## Historical development of the methods for sewer network calculation

#### Time valuation method

At first it was only a question of a suitable dimensioning of the pipe diameter. This is based on a rain shower line of a specified annual frequency of occurrence or return time of rain donations of increasing duration. At every location in the sewer network, the decisive factor is the donation whose duration corresponds to the flow time. The results can be seen regardless of the depth of the sewer network. Therefore, this method is completely unsuitable for flood detection as well as for basin dimensions.

#### Constant runoff coefficientor also sum line method

Pool dimensions possible, but no evidence of stowage. With this method, the runoff coefficient does not depend on the duration of the rain..

#### Variable runoff coefficient(Pecher)

With this method, complete drainage curves are calculated, so that limited basin dimensions are also possible

#### Surface runoff model

The dimensions of the pelvis and limited evidence of stowage and stowage are included. All of the methods mentioned so far are time-asymmetrical. Individual concepts are not useful with them and can be used economically, since these processes depict backwater situations more or less unrealistically. Appropriate calibrations are very often unsuccessful in trying to counteract process and data inaccuracies. Dami cannot be prevented from failing to increase errors in the results. For these reasons, from our point of view, these time-asymmetrical processes should also be avoided for dirt freight models with backwater relief structures.

#### Time-symmetrical [3D] sewer network calculation

The difference to the time-asymmetrical calculation is that the sewer network is not calculated in the chronological order from top to bottom or vice versa (e.g. energy line calculation in the surface runoff model or runoff coefficient method), but completely at all times. If the sewer network calculation is terminated prematurely, the network to be calculated is evenly and completely calculated until the time of the termination. In the case of a time-asymmetrical sewer network calculation, also called a hydrological method, only the upper part of the network is fully calculated, but this part over the complete simulation period. If you were to make a film that shows the load on the network at all times, you would not be able to tell in a time-symmetrical process whether it was running forwards or backwards; in the other case, of course, immediately, since the lower power supply units were the only ones running backwards would fill and finally the top ones. Time-symmetrical methods are of course characterized by a higher level of accuracy, since all network states can be viewed at the same time. The new network condition results from the old condition with a very fine temporal resolution by elementary mathematical solution of an initial boundary value problem, formulated by adhering to the volume, energy and momentum balance. For the first time, direct solutions to the equation of motion are brought into play according to the fundamental theorem of algebra, which is based on the complex numbers. Hence the name "Complexes Parallel Step Method" (CPM), which also represents an example of a classic implicit solution of the differential equation. In contrast to the time-asymmetrical methods, these time-symmetrical methods are very computing-intensive. For this reason, new approaches have been taken in recent years that bring the new multi-core processors (symmetrical multiprocessing) and distributed calculations on multiple computers (massive parallel computing) into play. The pioneer was tandler.com with the development of the complex parallel step procedure (CPM) within the channel network calculation KANAL ++ hydraulics, in which the computing times could be reduced so drastically that it is now possible to carry out series and long-term simulations with individual area data in such a way that Both the concerns of water protection and the concerns of flood protection can be considered and checked simultaneously for verification purposes. For the first time, the position coordinates of the positions or nodes and the assigned catchment areas are also considered functionally. A straight passage on the shaft causes less energy loss than a turn, e.g. 90 ° and this in turn less than when the medium is forced to flow in the opposite direction (180 °). These data are mostly available today via the common GIS systems (such as in KANAL ++ from tandler.com GmbH). However, the model also runs in a simplified manner without coordinates, as in general in all areas of the model the higher data complexity is not a "must" but a "can" and therefore the requirement for the data volume of conventional 1D methods (SWMM ...) is not exceeded. It can be seen from many practical examinations that calibrations are only necessary to correct too coarse or inaccurate data in the model using concrete measurements. This effort for calibration will be significantly reduced if increasingly accurate and individual data flow into the models (uneven irrigation, soil structure, surface characteristics). For the long-term forecast of the system behavior, the individualization of the data is not absolutely necessary in order to obtain a reliable estimate of the probabilities of contamination or flooding. This is the case with increased security, e.g. if the catchment area is only irrigated with a large area rain instead of a network of precipitation stations. However, the security achieved in this way is then distributed more evenly than if you try to obtain it using a method that is subject to deterministic errors - such as those that arise due to time asymmetry. Ultimately, this is at the expense of cost or security, or both.

#### GeoCPM: Time-symmetrical surface runoff calculation

Neither is related to the cost of using the complex parallel step method (CPM), which enables simultaneous implicit (2D) calculation of the surface (GeoCPM). This is bidirectionally coupled to the (3D) sewer network calculation. The drainage process in the sewer is also brought closer to reality in terms of its mapping accuracy. This is a further step in the direction of a comprehensive flood test or proof of flooding. In any case, the current limit of what is technically feasible for flood detection has been reached. It already provides a prototype for the use of the many CPUs that are found in today's modern graphics cards.

**This development of the sewer network calculations is reflected in the programs we offer.**

**The sewer network calculation methods and the calculation of surface water and surface runoff form the basis for the creation of a general drainage plan (GEP) or master plan for the corresponding sewer network and its associated waters.**

The general drainage plan is used as evidence of legal requirements for wastewater disposal, as a planning basis for new sewer networks and as a rehabilitation concept for existing sewer networks. For the first time, it is now possible to manage actual and planning states within a project file and to switch between the two states with a click of the mouse. At the same time, in the future a model will suffice for the two partially opposing protection objectives, for water protection on the one hand and flood protection on the other.