Robust shallow water models

Abstract

Shallow water models have been used extensively for decades with various applications in hydroscience and engineering such as flood prediction and management, river restoration and engineering, environmental hydraulics and morphodynamics. In recent years, there has been a special focus on developing robust solvers which are capable of simulating a wide range of complex hydrodynamic problems including dam breaks (shock propagation, wetting and drying, small water depths), as well as flow transitions (subcritical–supercritical flow and vice versa, hydraulic jumps). In addition to classical finite-volume and finite-element schemes, newer methods such as smoothed particle hydrodynamics (SPH) are now being applied and extended. Furthermore, we have seen rapid development in surveying techniques (e.g. airborne and terrestrial laser scanning) which describe the geometry and physical properties of our systems, providing us with increasingly high-resolution information. Substantial improvements have also been made in high-performance computing, with notable advances including Graphic Processing Unit (GPU)-based parallel computing as well as scaling methods, relying, for example, on frictionor porosity-based approaches. Linkage of robust numerical methods, highresolution data, high-performance computing, scaling methods and new information and communication technologies will lead to the next generation of shallow water models opening up new application fields such as rainfall– runoff simulation in urban and rural catchments, real-time flood and tsunami prediction and management, as well as the spreading of impulse water waves generated by landslides. In view of these developments, we have encouraged submissions on both the development of numerical models and interesting applications, for the XX International Conference on Computational Methods in Water Resources held on June 10–13, 2014 in Stuttgart, Germany, especially for the sessions on ‘Robust shallow water models’, ‘Numerical methods for waves, circulation and transport in the coastal Ocean’ and ‘High-performance computing, visualization and scientific workflow’. This special issue contains papers which have been selected by the guest editors among about 20 contributions. The corresponding authors have been offered the opportunity to contribute to this special issue through a paper about their conference contribution (abstract, oral, or poster presentation). The papers have all undergone a full peer-review process as regular journal submissions and, finally, we are happy to present this special issue consisting of ten papers. This special issue widens the already existing journal focus on shallow water models and their applications, see, for example, Delfs et al. (2013), Shi et al. (2014), Carbajal et al. (2014) or Huang et al. (2014). This special issue starts with two contributions dealing with floods. Beisiegel and Behrens (2015) have developed a robust discontinuous Galerkin (DG) model using special basis functions and a slope limiter. Flooding and drying is simulated through applying a stable scheme, and the model’s advantages are demonstrated in a numerical study. & Reinhard Hinkelmann reinhard.hinkelmann@wahyd.tu-berlin.de