A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: Triangular grids

A novel wetting and drying treatment for second-order Runge-Kutta discontinuous Galerkin (RKDG2) methods solving the non-linear shallow water equations is proposed. It is developed for general conforming two-dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a non-destructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well-balancing with an innovative velocity-based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme -- even on unstructured grids -- and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near-realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, super-linear convergence, mass-conservation, well-balancedness, and stability are verified

Triangular grids

A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified

Metrics for Performance Quantification of Adaptive Mesh Refinement

Non-uniform, dynamically adaptive meshes are a useful tool for reducing computational complexities for geophysical simulations that exhibit strongly localised features such as is the case for tsunami, hurricane or typhoon prediction. Using the example of a shallow water solver, this study explores a set of metrics as a tool to distinguish the performance of numerical methods using adaptively refined versus uniform meshes independent of computational architecture or implementation. These metrics allow us to quantify how a numerical simulation benefits from the use of adaptive mesh refinement. The type of meshes we are focusing on are adaptive triangular meshes that are non-uniform and structured. Refinement is controlled by physics-based indicators that capture relevant physical processes and determine the areas of mesh refinement and coarsening. The proposed performance metrics take into account a number of characteristics of numerical simulations such as numerical errors, spatial resolution, as well as computing time. Using a number of test cases we demonstrate that correlating different quantities offers insight into computational overhead, the distribution of numerical error across various mesh resolutions as well as the evolution of numerical error and run-time per degree of freedom

An adaptive discontinuous Galerkin method for the simulation of hurricane storm surge

Numerical simulations based on solving the 2D shallow water equations using a discontinuous Galerkin (DG) discretisation have evolved to be a viable tool for many geophysical applications. In the context of flood modelling, however, they have not yet been methodologically studied to a large extent. Systematic model testing is non-trivial as no comprehensive collection of numerical test cases exists to ensure the correctness of the implementation. Hence, the first part of this manuscript aims at collecting test cases from the literature that are generally useful for storm surge modellers and can be used to benchmark codes. On geographic scale, hurricane storm surge can be interpreted as a localised phenomenon making it ideally suited for adaptive mesh refinement (AMR). Past studies employing dynamic AMR have exclusively focused on nested meshes. For that reason, we have developed a DG storm surge model on a triangular and dynamically adaptive mesh. In order to increase computational efficiency, the refinement is driven by physics-based refinement indicators capturing major model sensitivities. Using idealised numerical test cases, we demonstrate the model’s ability to correctly represent all source terms and reproduce known variability of coastal flooding with respect to hurricane characteristics such as size and approach speed. Finally, the adaptive mesh significantly reduces computing time with no effect on storm waves measured at discrete wave gauges just off the coast which shows the model’s potential for use as a robust simulation tool for real-time predictions

Numerical Testcases to Study Proudman Resonance Using Shallow Water Models

Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with respect to represent mentioned resonance. With the test cases we assess the wave amplification in dependence of characteristics of the pressure perturbation, model parameters, model resolution, and bathymetry characteristics. We use the compilation of tests to validate an adaptive discontinuous Galerkin (DG) model for the two-dimensional non-linear shallow water equations. As the tests are highly sensitive to model resolution, we use the adaptive mesh capabilities of the model to locally refine the disturbance and thus gain considerable efficiency

An Experimental and Numerical Study of Long Wave Run-Up on a Plane Beach

This research is to facilitate the current understanding of long wave dynamics at coasts and during on-land propagation, experimental and numerical approaches are compared against existing analytical expressions for the long wave run-up. Leading depression sinusoidal waves are chosen to model these dynamics. The experimental study was conducted using a new pump-driven wave generator and the numerical experiments were carried out with a one-dimensional discontinuous Galerkin non-linear shallow water model. The numerical model is able to accurately reproduce the run-up elevation and velocities predicted by the theoretical expressions. Depending on the surf similarity of the generated waves and due to imperfections of the experimental wave generation, riding waves are observed in the experimental results. These artifacts can also be confirmed in the numerical study when the data from the physical experiments is assimilated. Qualitatively, scale effects associated with the experimental setting are discussed. Finally, shoreline velocities, run-up and run-down are determined and shown to largely agree with analytical predictions

Systematic Review Shows That Work Done by Storm Waves Can Be Misinterpreted as Tsunami-Related Because Commonly Used Hydrodynamic Equations Are Flawed

Coastal boulder deposits (CBD), transported by waves at elevations above sea level and substantial distances inland, are markers for marine incursions. Whether they are tsunami or storm deposits can be difficult to determine, but this is of critical importance because of the role that CBD play in coastal hazard analysis. Equations from seminal work by Nott (1997), here referred to as the Nott Approach, are commonly employed to calculate nominal wave heights from boulder masses as a means to discriminate between emplacement mechanisms. Systematic review shows that this approach is based on assumptions that are not securely founded and that direct relationships cannot be established between boulder measurements and wave heights. A test using an unprecedented dataset of boulders moved by storm waves (with associated sea-state data) shows a lack of agreement between calculations and actual wave heights. The equations return unrealistically large heights, many of which greatly exceed sea states occurring during the boulder-moving storms. This underscores the finding that Nott-Approach wave-height calculations are unreliable. The result is general, because although the field data come from one region (the Aran Islands, Ireland), they represent a wide range of boulder masses and topographic settings and present a valid test of hydrodynamic equations. This analysis demonstrates that Nott Approach equations are incapable of distinguishing storm waves from tsunami transport and that wave heights hindcast from boulder masses are not meaningful. Current hydrodynamic understanding does not permit reliable computation of wave height from boulder measurements. A combination of field, numerical, and experimental approaches is required to quantify relationships between wave power and mass transport onshore. Many CBD interpreted as tsunami deposits based on Nott-Approach analysis may in fact have been emplaced during storms and should therefore be re-evaluated. This is especially important for CBD that have been incorporated into long-term coastal risk assessments, which are compromised if the CBD are misinterpreted. CBD dynamics can be better determined from a combination of detailed field measurements, modeling, and experiments. A clearer understanding of emplacement mechanisms will result in more reliable hazard analysis

Stewards of Integrity: Institutional Approaches to Promote and Safeguard Good Research Practice in Europe

56 pages.In December 2000, the European Science Foundation published a Science Policy Briefing entitled Good Scientific Practice in Research and Scholarship. The time was not coincidental. During the 1990s, there were many major cases of research misconduct that were widely publicised in both the scientific and general media.As research organisations in various countries were undertaking efforts to tackle the problem, there was a need to learn from each other’s experiences and with the idea of the European Research Area (ERA) then burgeoning, discussions began on whether there should be coordinated efforts at the European level.The ESF Science Policy Briefing No. 10 surveyed the then existing policies and practices in Europe and discussed the responsibilities of researchers and research organisations. It called upon ESF Member Organisations, to act, in their diverse roles, as stewards of research integrity.To this end, the European Science Foundation collected information from its Member Organisations and other relevant bodies, and this resulting report presents the policies, approaches and practices to foster good scientific practice found in several European countries.Although the report is not exhaustive both in terms of countries and institutions covered, it provides a basis for an overview of mechanisms to promote good research practice and to handle cases of alleged research misconduct that exist in different European countries.This work and publication was part-funded by the European Commission (Contract No GNBL-2007-00002).Peer reviewe

Aquatische Optische Technologien in Deutschland

Optische Technologien und Verfahren sind sowohl in der limnischen als auch marinen Forschung Deutschlands über alle Bereiche und Skalen etabliert und entwickeln sich rasant weiter. Die Arbeitsgruppe „Aquatische Optische Technologien“ (AOT) will Forschern und Anwendern eine Plattform bieten, die Wissenstransfer fördert, der nationalen Entwicklergemeinschaft ein synergistisches Umfeld eröffnet und die internationale Sichtbarkeit der deutschen Aktivitäten in diesem Forschungsfeld erhöht. Diese Zusammenfassung dokumentiert erstmalig die AOT-Verfahren und -Technologien, die von nationalen Forschungsinstitutionen eingesetzt werden. Wir erwarten, dass die Dokumentation einen Trend in Richtung institutsübergreifender Harmonisierung initiiert. Dies wird die Etablierung offener Standards, eine Verbesserung im Zugang zu Dokumentationen und gegenseitige technischer Hilfestellung bei (System-) Integrationen ermöglichen. Effizienz und Leistungsfähigkeit der AOT-Entwicklung und Anwendung auf nationaler Ebene werden von diesen Bestrebungen profitieren. Weitere Arbeitsgruppen und Entwickler werden ausdrücklich ermutigt, Kontakt aufzunehmen, um in einer späteren Auflage berücksichtigt zu werden