Coarse grid approaches for the shallow water model

Current developments in survey technology such as LIDAR and laser scanning are able to deliver high resolution data sets at relative low cost. However, simulations on the scale of these data sets is only feasible on super-computers. Especially in explicit Godunov type schemes the computational effort increases proportional to the grid resolution.

Aim of research is to develop model concepts for shallow water models which allow to coarsen the grid size of a numerical model while still maintaining an acceptable accuracy.

A very intuitive approach for grid coarsening is to calibrate the coarse grid model via the friction coefficient. Indeed, this is physically reasonable because the friction coefficient itself is defined as a conceptual description of unresolved structures.

In this research work, we derived a solely mathematical friction law-based approach that contains three parameters to describe the unresolved geometry.

This approach is published in Özgen et al. (2015).

A common approach in literature is the extension of the shallow water equations with porosity terms. The porosity describes the fraction of the cell available to flow. The so-called anisotropic porosity shallow water equations use additional porosities at the cell edges.

We extended the anisotropic porosity shallow water equations with water depth-dependent porosity terms, thus allowing full submergence of unresolved topography. 

The equations are published in Özgen et al. (2016a). Numerical studies of model properties have been published in Özgen et al. (2016b).

The shallow water equations with isotropic porosity use solely one porosity term per cell. The porosity term describes the fraction of the cell available to flow.

We implemented a lateralized finite-volume scheme for the solution of the isotropic porosity shallow water equations.

The following figure shows a well-known benchmark for verifying the numerics, the dam-break through a channel with a constant porosity gradient.

The implemented scheme is able to reproduce the quasi-analytical solution well enough.

in preparation

Özgen, I., Bruwier, M., Zhao, J., Liang, D. & Hinkelmann, R.: Numerical study of building drag dissipation formulations in the integral porosity shallow water model. Submitted: River Flow 2018, Special session on porosity models, Lyon-Villeurbanne, Frankreich.

Özgen, I., Amann, F., Abily, M., Zhao, J., Liang, D., Gourbesville, P. & Hinkelmann, R.: Integral porosity shallow water model at district scale - Case study of a district in Nice. Submitted: River Flow 2018, Special session on porosity models, Lyon-Villeurbanne, Frankreich.

Özgen, I., Abily, M., Gourbesville, P., Zhao, J., Liang, D. & Hinkelmann, R.: Towards district scale flood simulations using conventional and integral porosity shallow water models with high-resolution topographic information. Submitted: La Houille Blanche.

Özgen, I., Zhao, J., Kim, B., Liang, D. & Hinkelmann, R.: An anisotropic-porosity shallow water model with novel monotonicity treatment and subgrid-scale drag estimation, Submitted: International Journal for Numerical Methods in Fluids

2017

Doctoral thesis

Özgen, I.: Coarse grid approaches for the shallow water model, Doctoral thesis, Technische Universität Berlin, Berlin, Germany.

Journals

Özgen, I., Zhao, J., Liang, D. & Hinkelmann, R.: Wave propagation speeds and source term influence in single and integral porosity shallow water equations, Water Science and Engineering, in press.

Conferences

Özgen, I.: Coarse grid modeling concepts for rainfall-runoff simulations. In: 37th IAHR World Congress 2017, 13.8.-18.8.2017, Kuala Lumpur, Malaysia.

Oral presentations

Özgen, I., Liang, D. & Hinkelmann, R.: Stability and convergence of the integral porosity shallow water model, Oral presentation at UWI Summer School 2017, Kremmen, Germany.

Hinkelmann, R., Özgen, I., Zhao, J., Teuber, K. & Liang, D.: Scaling of shallow water models, Oral presentation at Xi'an University of Technology, Xi'an, China.

Hinkelmann, R., Özgen, I., Zhao, J., Teuber, K. & Liang, D.: Scaling of shallow water models, Oral presentation at BIMoS Day: Shallow Water Flow Simulations, Berlin International Graduate School in Model and Simulation based Research, Berlin, Germanyq.

2016

Journals

Özgen, I., Zhao, J., Liang, D. & Hinkelmann, R.: Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. Journal of Hydrology 541, pp. 1165-1184. doi: 10.1016/j.hydrol.2016.08.025

Özgen, I., Liang, D. & Hinkelmann, R.: Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography. Applied Mathematical Modelling 40, pp. 7447-7473. doi: 10.1016/j.apm.2015.12.012

Conferences

Özgen, I., Serrano-Taslim, M., Zhao, J., Liang, D. & Hinkelmann, R.: Coarse grid shallow water simulations of rainfall-runoff in small catchments with modified friction law to account for unresolved microtopography. In: European Geophysical Union General Assembly 2016, 17.-22.4.2016, Vienna, Austria, poster

Özgen, I., Liang, D., Om, J. & Hinkelmann, R.: Shallow water model with anisotropic porosity: A case study of dam-break flow in city environment. In: 12th International Conference on Hydroinformatics, 21.-26.8.2016, Incheon, South Korea

Oral presentations

Özgen, I., Zhao, J., Liang, D. & Hinkelmann, R.: Comparison of an isotropic porosity shallow water model with an anisotropic porosity shallow water model. Oral presentation at Nordic Water Network Conference 2016, Berlin, Germany.

Hinkelmann, R., Özgen, I., Zhao, J., Teuber, K. & Liang, D.: Coarse grid strategies for computationally efficient flash flood simulations. Oral presentation at 2nd International Symposium on Flash Floods in Wadi Systems 2016, El Gouna, Egypt.

Özgen, I., Zhao, J., Liang, D. & Hinkelmann, R.: Towards an anisotropic porosity shallow water model for computationally efficient rainfall-runoff simulation. Oral presentation at Doktorandenworkshop Hydrologische Modellierung, 23.-24.6.2016, Freie Universität Berlin, Berlin, Germany

Özgen, I., Zhao, J., Liang, D. & Hinkelmann, R.: Some observations on the shallow water equations with depth-dependent anisotropic porosity. Oral presentation at Kollegiate day of the DFG Research Training Group  Urban Water Interfaces, 22.9.2016, Technische Universität Berlin, Berlin, Deutschland.

2015

Journals

Özgen, I., Teuber, K., Simons, F., Liang, D. & Hinkelmann, R.: Upscaling the shallow water model with a novel roughness formulation. Environmental Earth Sciences 74(11), pp. 7371-7386. doi: 10.1007/s12665-015-4726-7

Conferences

Özgen, I., Liang, D., & Hinkelmann, R.: Shallow water equations with anisotropic porosity for inundated areas. Workshop on Advances in Numerical Modelling of Hydrodynamics, 24.-25.3.2015, Sheffield, UK, reviewed paper and oral presentation

Özgen, I., Teuber, K., Liang, D., & Hinkelmann, R.: Surface roughness parameterization to account for subgrid-scale topography in shallow water modeling. E-proceedings of the 36th IAHR World Conference, 28.6.-3.7.2015, Den Haag, the Netherlands, reviewed paper and oral presentation

Oral presentations

Hinkelmann, R., Özgen, I., Teuber, K. & Liang, D.: Coarse grid methods for flood models. Oral presentation at Kobe University, Kobe, Japan, on 15.9.2015

Hinkelmann, R., Özgen, I., Teuber, K. & Liang, D.: Coarse grid methods for flood models. Oral presentation at Kyoto City Disaster Prevention Center, Kyoto, Japan on 18.9.2015

2014

Conferences

Özgen, I., Simons, F., & Hinkelmann, R.: Fully dynamic two-dimensional shallow water equations based simulation of urban runoff in a simplified catchment. Computational Methods in Water Resources, XX. International Conference, 10.-13.6.2014, Stuttgart, Germany, extended abstract and oral presentation

in progress

Amann, F.: Urban flood modeling in a district of Nice, France. Student research project in the master program civil engineering.

2017

Reports

Amann, F.: Reduced complexity strategies for urban flood modeling. Student report for the module Colloquium Hydrosciences.

2016

Bachelor theses

Serrano Taslim, M.: Application of a friction law-based coarse grid approach for the shallow water model: Case studies of rainfall-runoff events in small natural catchments. Thesis in the bachelor program civil engineering.

2015

Master theses

Teuber, K.: Development of a scaling approach to account for microtopography in the shallow water equations. Thesis in the master program civil engineering with specialization in hydrosciences.

2014

Student research projects

Teuber, K.: Numerische Simulation von Niederschlags-Abfluss-Ereignissen in einem vereinfachten urbanen Einzugsgebiet unter Berücksichtigung von lokalen Depressionen. Student research project in the master program civil engineering.

Müller, S.: Parameterstudie eines Niederschlag-Abfluss-Ereignisses in einem vereinfachten urbanen Einzugsgebiet hinsichtlich Rauhigkeit, Gefälle und Niederschlagsintensität.  Student research project in the master program civil engineering.

Müller, S.: Wasserstandentwicklung für konstante Niederschlagsereignisse in einem geschlossenen Einzugsgebiet.  Extended student research project in the master program civil engineering.

This work is funded by Technische Universität Berlin.

Conference participation has been (partially) funded by:

• Gesellschaft von Freunden der TU Berlin e.V.
• DFG Graduiertenkolleg Urban Water Interfaces

Numerical simulations have been realized on the computers of the Norddeutsche Verbund für Hoch- und Höchstleistungsrechnen (HLRN).

Special thanks to

• apl. Prof. Dr.-Ing. Frank Molkenthin, Brandenburgische Technische Universität Cottbus-Senftenberg
• Prof. Dr. Philippe Gourbesville, Université Nice Sophia Antipolis

for their support and suggestions.

Further, we thank

• Prof. Dr. Andrea Defina, Università degli Studi di Padova
• Dr. Martin Bruwier, Université de Liège
• Dr. Martin Fišer, Západočeská univerzita v Plzni
• Dr. Daniel Caviedes-Voullième, Brandenburgische Technische Universität Cottbus-Senftenberg
• Dr. Morgan Abily, Université Nice Sophia Antipolis

for the insightful discussions.