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In many natural disasters such as overland oil spills or lava flows, physical fluid properties as density change when considering non-homogeneous spatial and time variable distributions of the temperature. This effect is even more remarkable when these flows show a non-Newtonian behaviour due to the sensitivity of their rheological properties as viscosity or yield stress to temperature. In these cases, temperature becomes a significant variable that drives the fluid behaviour, which must be solved using an energy equation coupled with the free surface flow system. Special attention is devoted to thermal source terms which must include all the heat fluid exchanges, and their modelling sometimes can govern the complete flow behaviour. Fluid density, viscosity and yield stress, also affected by temperature, must be recomputed every time step. Summarizing, this work presents a 2D free surface flow model considering density and temperature variations, which could even modify viscosity and yield stress, with heat transfer mechanisms. The model is applied to oil spill overland simulations and heating/cooling test cases are carried out to ensure the system energy balance. As conclusions, it can be said that the numerical results demonstrate the importance of the heat exchange effects and those of the density, viscosity and yield stress variations.

Finite Volume Non-Hydrostatic Pressure (NHP) Model for the Simulation of Landslides

A Finite Volume (FV) numerical scheme previously designed for the hydrostatic Shallow Water Equations (SWE) is extended to compute non-hydrostatic pressure (NHP) in order to simulate dispersive waves. These waves are usually generated by landslides and are of importance in coastal alarm systems. The model is validated in 1D comparing with laboratory measurements and the results highlight the importance of including the NHP terms in the model to achieve a good agreement between numerical and experimental results.

15 figures, 2 tables., In this study, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed., This work was funded by the Spanish Ministry of Science and Innovation under the research project PGC2018-094341-B-I00. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

15 figures, 1 table., Coupled 1D2D models emerged as an efficient solution for a two-dimensional (2D) representation of the floodplain combined with a fast one-dimensional (1D) schematization of the main channel. At the same time, high-performance computing (HPC) has appeared as an efficient tool for model acceleration. In this work, a previously validated 1D2D Central Processing Unit (CPU) model is combined with an HPC technique for fast and accurate flood simulation. Due to the speed of 1D schemes, a hybrid CPU/GPU model that runs the 1D main channel on CPU and accelerates the 2D floodplain with a Graphics Processing Unit (GPU) is presented. Since the data transfer between sub-domains and devices (CPU/GPU) may be the main potential drawback of this architecture, the test cases are selected to carry out a careful time analysis. The results reveal the speed-up dependency on the 2D mesh, the event to be solved and the 1D discretization of the main channel. Additionally, special attention must be paid to the time step size computation shared between sub-models. In spite of the use of a hybrid CPU/GPU implementation, high speed-ups are accomplished in some cases., This work is part of the PGC2018-094341-B-I00 research project funded by the Ministry of Science and Innovation/FEDER. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

A one-dimensional (1D) numerical model for the simulation of oil spills in coastal flows is studied. A two-layer eulerian model is implemented. The main advantage of this model is the capability of solving the evolution of the oil layer, computing the oil depth and the velocity field.

There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.

19 Pags.- 10 Figs.- 3 Tabls., River floods can be simulated with the 2D shallow water system of equations using finite volume methods, where the terrain is discretized in cells that form the computational mesh. Usually a proper treatment of wet/dry fronts is required. River levees can be modelled as part of the topography by means of sufficiently small cells of higher elevation than the rest of the bed level in locally refined meshes. This procedure is associated with a large computational time since the time step depends directly on the cell size. The alternative proposed in this work includes the levees as internal boundary conditions in the 2D numerical scheme. In particular, levees have been defined by a weir law that, depending on the relative values of water surface levels on both sides, can formulate the discharge for different situations (i.e. free flow and submerged flow). In addition, having identified numerical difficulties in cases of low discharge under free flow conditions, a novel procedure to avoid oscillations has been developed and called volume transport method. The validation and comparison between methods has been carried out with benchmark test cases and, in addition, with a real flood event in the Ebro River (Spain), This work was partially funded by the MINECO/FEDER under research Project CGL2015-66114-R and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER. The third author also wants to thank to the MINECO for his Research Grant DI-14-06987.

18 Pags.- 11 Figs.- 2 Tabls., The numerical modelling of 2D shallow flows in complex geometries involving transient flow and movable boundaries has been a challenge for researchers in recent years. There is a wide range of physical situations of environmental interest, such as flow in open channels and rivers, tsunami and flood modelling, that can be mathematically represented by first-order non-linear systems of partial differential equations, whose derivation involves an assumption of the shallow water type. Shallow water models may include more sophisticated terms when applied to cases of not pure water floods, such as mud/debris floods, produced by landslides. Mud/debris floods are unsteady flow phenomena in which the flow changes rapidly, and the properties of the moving fluid mixture include stop and go mechanisms. The present work reports on a numerical model able to solve the 2D shallow water equations even including bed load transport over erodible bed in realistic situations involving transient flow and movable flow boundaries. The novelty is that it offers accurate and stable results in realistic problems since an appropriate discretization of the governing equations is performed. Furthermore, the present work is focused on the importance of the computational cost. Usually, the main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in realistic cases. However, the proposed model is able to reduce computer times by orders of magnitude making 2D applications competitive and practical for operational flood prediction. Moreover our results show that high performance code development can take advantage of general purpose and inexpensive Graphical Processing Units, allowing to run almost 100 times faster than old generation codes in some cases., This work was partially funded by the MINECO/FEDER under research project CGL2015-66114-R and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER. The third author also wants to thank to the MINECO for his Research Grant DI-14-06987.

One dimensional (1D) shallow water models are widely used for prediction purposes to assess and help river basin administrations and public authorities in the decision-making process. However, their results can be inaccurate since the hypotheses underlying the 1D model are not satisfied during flooding events. On the other hand, two-dimensional (2D) models offer more information to follow the inundation process and the flow properties over floodplains. Despite the well- known higher computational cost of 2D models, they have gained popularity since they can be implemented under GPU cards that allow faster computations, providing more information than 1D models. In this work, two flooding events in the Ebro River (Spain) are analyzed to evaluate the performance of both 1D and 2D shallow water models.

The challenge of finding a compromise between computational time and level of accuracy and robustness has traditionally expanded the use simplified models rather than full two-dimensional (2D) models for flood simulation. This work presents a GPU accelerated 2D shallow water model for the simulation of flood events in real time. In particular, an explicit first-order finite volume scheme is detailed to control the numerical instabilities that are likely to appear when used in complex topography. The model is first validated with the benchmark test case of the Toce River (Italy) and numerical fixes are demonstrated to be necessary. The model is next applied to reproduce real events in a reach of the Ebro River (Spain) in order to compare simulation results with field data. The second case deals with a large domain (744 km2) and long flood duration (up to 20 days) allowing an analysis of the performance and speed-up achieved by different GPU devices. The high values of fit between observed and simulated results as well as the computational times achieved are encouraging to propose the use of the model as forecasting system.

8 pags.- 5 Figs. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Modern flood risk management and mitigation plans incorporate the presence of numerical models that are able to assess the response of the system and to help in the decision-making processes. The shallow water system of equations (SWE) is widely used to model free surface flow evolution in river flooding. Although 1D models are usually adopted when simulating long rivers due to their computational efficiency, 2D models approximate better the behaviour in floodplains of meandering rivers using a fine mesh which implies unaffordable computations in real-world applications. However, the advances on parallelization methods accelerate computation making 2D models competitive. In particular, GPU technology offers important speed-ups which allow fast simulations of large scale scenarios. In this work, an example of the scope of this technology is presented. Several past flood events have been modelled using GPU. The physical domain (middle part of the Ebro River in Spain) has a extent of 477 km2, which gives rise to a large computational grid. The steps followed to carry out the numerical simulation are detailed, as well as the comparison between numerical results and observed flooded areas reaching coincidences up to 87.25 % and speed enhancements of 1-h of simulation time for 1-day flood event. These results lead to the feasible application of this numerical model in real-time simulation tools with accurate and fast predictions useful for flood management.

[EN] A study of measures oriented to flood mitigation in the mid reach of the Ebro river is presented: elimination of vegetation in the riverbed, use of controlled flooding areas and construction or re-adaptation of levees. The software used is RiverFlow2D which solves the conservative free-surface flow equations with a finite volume method running on GPU. The results are compared with measurements at gauge stations and aerial views. The most effective measure has turned out to be the elimination of vegetation in the riverbed. It is demonstrated that not only the maximum flooded area is narrower but also it reduces the water depth up to 1 m. The other measures have local consequences when the peak discharge is relatively high although they could be useful in case the discharge is lower, [ES] En este trabajo se presenta un estudio de medidas orientadas a la mitigación de avenidas en el tramo medio del río Ebro: limpieza de vegetación del cauce, uso de zonas de inundación controlada y construcción o re-adaptación de motas. Para ello se utiliza el software RiverFlow2D que resuelve las ecuaciones conservativas del flujo de superficie libre con un método de volúmenes finitos realizando los cálculos sobre GPU. Se comparan los resultados con medidas en estaciones de aforo e información extraída de ortofotos. La medida más efectiva, de las analizadas, ha resultado ser la eliminación de la vegetación en el cauce. Se demuestra que no sólo el área máxima inundada es menor en todo el tramo sino que también reduce la altura de agua hasta en 1 m. El resto de medidas tienen consecuencias locales y de poca entidad cuando los caudales pico son altos, aunque podrían resultar de utilidad para avenidas con caudales más bajos., Este trabajo se encuentra en el marco del proyecto de investigación CGL2015-66114-R financiado por el Ministerio de Ciencia e Innovación/FEDER. Los autores quieren agradecer también a la Confederación Hidrográfica del Ebro por su disponibilidad de consulta y gestión de datos.