Danko Holjević

Numerical Simulations of Water Wave Propagation and Flooding

In this paper we present main points in the process of application of numerical schemes for hyperbolic balance laws to water wave propagation and flooding. The appropriate mathematical models are the one-dimensional open channel flow equations and the two-dimensional shallow water equations. Therefore good simulation results can only be obtained with well-balanced numerical schemes such as the ones developed by Bermudez and Vazquez, Hubbard and Garcia-Navarro, LeVeque, etc. as well as the ones developed by the authors of this paper. We also propose a modification of the well-balanced Q-scheme for the two-dimensional shallow water equations that solves the wetting and drying problem. Finally, we present numerical results for three simulation tasks: the CADAM dam break experiment, the water wave propagation in the Toce river, and the catastrophic dam break on the Malpasset river.

Floods in the Danube River Basin in Croatia in 2010

The recent decades have witnessed very intensive rainfalls throughout Europe which resulted in flood waves in rivers that reached or sometimes even exceeded the maximum water levels recorded to date. In the Danube River basin in Croatia, such a year was 2010, which was defined in terms of precipitation as an extremely wet, very wet, or wet year in 99% of the territory. Between 30 May and 2 June, precipitation reached record quantities of up to 180 mm over most of Slavonia, and again, between 20 June and 23 June additional 90–100 mm of rain fell (the highest daily precipitation, 107.2 mm, was measured in Osijek). Snow melting due to sudden warming at the end of December 2009 and beginning of January 2010 also contributed to the formation of two large water waves not only on the Danube, Sava, and Drava Rivers but also on their numerous minor tributaries. Despite timely undertaken defence measures, embankments were breached at some critical locations, with water uncontrollably flooding the floodplains and causing heavy damages. This chapter presents key flood events and the lessons learned from them.