A family of well-balanced WENO and TENO schemes for atmospheric flows

We herein present a novel methodology to construct very high order well-balanced schemes for the computation of the Euler equations with gravitational source term, with application to numerical weather prediction (NWP). The proposed method is based on augmented Riemann solvers, which allow preserving the exact equilibrium between fluxes and source terms at cell interfaces. In particular, the augmented HLL solver (HLLS) is considered. Different spatial reconstruction methods can be used to ensure a high order of accuracy in space (e.g. WENO, TENO, linear reconstruction), being the TENO reconstruction the preferred method in this work. To the knowledge of the authors, the TENO method has not been applied to NWP before, although it has been extensively used by the computational fluid dynamics community in recent years. Therefore, we offer a thorough assessment of the TENO method to evidence its suitability for NWP considering some benchmark cases which involve inertia and gravity waves as well as convective processes. The TENO method offers an enhanced behavior when dealing with turbulent flows and underresolved solutions, where the traditional WENO scheme proves to be more diffusive. The proposed methodology, based on the HLLS solver in combination with a very high-order discretization, allows carrying out the simulation of meso- and micro-scale atmospheric flows in an implicit Large Eddy Simulation manner. Due to the HLLS solver, the isothermal, adiabatic and constant Brunt-Väisälä frequency hydrostatic equilibrium states are preserved with machine accuracy

2D numerical simulation of unsteady flows for large scale floods prediction in real time

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

Analysis of the performance of a hybrid CPU/GPU 1D2D coupled model for real flood cases

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

Use of internal boundary conditions for levees representation: application to river flood management

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)

The shallow water equations and their application to realistic cases

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

A model for computing thermally-driven shallow flows

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

RiverFlow2D numerical simulation of flood mitigation solutions in the Ebro River

[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.Echeverribar, I.; Morales-Hernández, M.; Lacasta, A.; Brufrau, P.; García-Navarro, P. (2017). Simulación numérica con RiverFlow2D de posibles soluciones de mitigación de avenidas en el tramo medio del río Ebro. Ingeniería del Agua. 21(1):53-70. https://doi.org/10.4995/ia.2017.6550SWORD5370211Ahmad, S., Simonovic, S. 2006. An intelligent decision support system for management of floods. Water Resources Management, 20(3), 391-410. doi:10.1007/s11269-006-0326-3Ahmadian, R., Falconer, R. A., Wicks, J. 2015. Benchmarking of flood inundation extent using various dynamically linked one- and two-dimensional approaches. Journal of Flood Risk Management, 1-15. doi:10.1111/jfr3.12208Bates, P. D., De Roo, A. P. J. 2000. A simple raster-based model for flood inundation simulation. Journal of Hydrology, 236(1-2), 54-77. doi:10.1016/S0022-1694(00)00278-XBladé, E., Cea, L., Corestein, G., Escolano, E., Puertas, J., Vázquez-cendón, E., Dolz, J., Coll, A. 2014. Iber: herramienta de simulación numérica del flujo en ríos. Revista internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 30(1), 1-10. doi:10.1016/j.rimni.2012.07.004Brufau, P., García-Navarro, P. 2001. Modelo de simulación bidimensional de transitorios en aguas superficiales: aplicación a roturas de presa. Ingeniería Civil, 121, 33-40.Caviedes-Voullième, D., Morales-Hernández, M., López-Marijuan, I., García-Navarro, P. 2014. Reconstruction of 2D river beds by appropriate interpolation of 1D cross-sectional information for flood simulation. Environmental modelling & software, 61, 206-228. doi:10.1016/j.envsoft.2014.07.016Comisión Técnica del Comité Español de la Estrategia Internacional para la Reducción de Desastres, Dirección general de protección civil y emergencias, Ministerio del interior, Gobierno de España. Reducción del riesgo de desastres, nº 3 enero-abril 2016. http://www.proteccioncivil.org.DHI. 2009. MIKE 21 Flow Model. Hydrodynamic Module Scientific Documentation. MIKE by DHI, 2009.García, R., Restrepo, P., Deweese, M., Ziemer, M., Palmer, J., Thornburg, J., Murillo, J., Morales, M., García-Navarro, P., Lacasta, A. 2015. Advanced GPU Parallelization for two-dimensional operational river flood forecasting. Proceedings of the 36th IAHR World Congress, Junio 28-Julio 3. The Hague, The Netherlands.Lacasta, A., Morales-Hernández, M., Murillo, J., García-Navarro, P. 2014. An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes. Advances in engineering software, 78, 1-15. doi:10.1016/j.advengsoft.2014.08.007Lacasta, A., Juez, C., Murillo, J., García-Navarro, P. 2015. An efficient solution for hazardous geophysical flows simulation using GPUs. Computers & Geosciences, 78, 63-72. doi:10.1016/j.cageo.2015.02.010Morales-Hernández, M., García-Navarro, P., Burguete, J., Brufau, P. 2013. A conservative strategy to couple 1D and 2D models for shallow water flow simulation. Computers & Fluids, 81, 26-44. doi:10.1016/j.compfluid.2013.04.001Murillo, J., Brufau, P., García-Navarro, P., Rodríguez, M., Andrés-Urrutia, A. 2007. A mathematical model for numerical simulation of shallow water flow: description and practical application of Guad2D. Proceedings of the Environmental Informatics and System Research Congress (Enviroinfo 2007), September 12-14, Warsaw, Poland, 409-416.Plan de Gestión del Riesgo de Inundación, Confederación Hidrográfica del Ebro. http://www.chebro.es/PGRI. Último acceso: enero 2017.Roe, P. L. 1981. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics, 43(2), 357-372. doi:10.1016/0021-9991(81)90128-5Shang, Z. 2014. High performance computing for flood simulation using Telemac based on hybrid MPI/OpenMp parallel programming. International Journal of modeling, simulation and scientific computing, 5(4), 1-13.Suman, A., Akther, F. 2014. River Flood Modelling Using SOBEK: A Case Study from Ciliwung Catchment, Indonesia. International Journal of Engineering Research, 3(11), 662- 668. doi:10.17950/ijer/v3s11/1108Toriman, M.E., Hassan, A.J., Gazim, M.B., Mokhtar, M., Mastura, S.A., Jaafar, O., Karim, O., Aziz, N.A. 2009. Integration of 1-d Hydrodynamic Model and GIS Approach in Flood Management Study in Malaysia. Research Journal of Earth Sciences, 1(1), 22-27.Van der Knijff, J.M., Younis, J., De Roo, A.P.J. 2010. LISFLOOD: a GIS-based distributed model for river basin scale water balance and flood simulation. International Journal of Geographical Information Science, 24(2), 189-212. doi:10.1080/1365881080254915

A fully Eulerian two-layer model for the simulation of oil spills spreading over coastal flows

Nowadays, the vast majority of coastal oil spill simulation models are based on Lagrangian methods focused on particle tracking algorithms to represent the oil slick fate. In this work, a fully Eulerian numerical model for the simulation of such environmentally significant disaster is implemented by means of a two-dimensional two-layer shallow water model. A very thin oil layer over a thicker water layer is considered in order to neglect the pressure term that the oil layer exerts over the water. Friction terms between layers are responsible for the layers coupling so that the oil layer flows over a moving water volume. To complete this dynamic model, the temperature transport and evolution under heat exchange for the oil upper layer is considered and the weathering process of evaporation is included. The numerical solution adopted is based on a finite volume upwind scheme with a Roe solver for both oil and water layers. Special care has been taken on the numerical treatment of the two-layer wet-dry boundaries (oil–water–land) and friction terms, since the objective of the model is to compute the oil slick front advancing near the coast

Extension of a Roe-type Riemann solver scheme to model non-hydrostatic pressure shallow flows

The aim of this work is, first of all, to extend a finite volume numerical scheme, previously designed for hydrostatic Shallow Water (SWE) formulation, to Non Hydrostatic Pressure (NHP) depth averaged model. The second objective is focused on exploring two available options in the context of previous work in this field: Hyperbolic-Elliptic (HE-NHP) formulations solved with a Pressure-Correction technique (PCM) and Hyperbolic Relaxation formulations (HR-NHP). Thus, besides providing an extension of a robust and well-proved Roe-type scheme developed for hydrostatic SWE to solve NHP systems, the work assesses the use of first order numerical schemes in the kind of phenomena typically solved with higher order methods. In particular, the relative performance and differences of both NHP numerical models are explored and analysed in detail. The performance of the models is compared using a steady flow test case with quasi-analytical solution and another unsteady case with experimental data, in which frequencies are analysed in experimental and computational results. The results highlight the need to understand the behaviour of a parameter-dependent model when using it as a prediction tool, and the importance of a proper discretization of non-hydrostatic source terms to ensure stability. On the other hand, it is proved that the incorporation of a non-hydrostatic model to a shallow water Roe solver provides good results

A 2D shallow water flow model with 1D internal boundary condition for subgrid-scale topography

In this work, a dynamic internal boundary condition is used as subgrid model in a two-dimensional (2D) model based on the shallow water equations in order to model narrow regions in the domain. In this way, computational savings are sought, since it is not necessary to discretize these regions with cells of reduced size. The new internal boundary condition simplifies other works where 1D-2D coupled models were presented, since the 1D model is a subgrid for the 2D mesh, so the coupling between both models is simple and direct. The coupling is performed using mass conservation, simplifying the calculation in the transfer between both models. Test cases are studied to validate the implemented boundary condition, and a mountain catchment as a realistic case. The results obtained with a fully 2D mesh and a 2D mesh with rills in narrow regions are very similar, with a large reduction in computational cost when using rills, both in test cases and in the realistic case. Thus, the use of the implemented internal boundary condition is an effective tool to study regions with narrow regions by reducing the computational cost with little loss of accuracy in the results