Mario Morales-Hernández

An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes

A GPU implementation of a FV method for the 2D Shallow Water Equations is presented.Structured and unstructured meshes allow different implementations.NVIDIA C2070 GPU is compared against Intel Core 2 Quad Processor.The basic GPU implementation obtains between 20× and 30× of speed-up.Some strategies on the mesh order allow to double the performance, reaching 50×. This work is related with the implementation of a finite volume method to solve the 2D Shallow Water Equations on Graphic Processing Units (GPU). The strategy is fully oriented to work efficiently with unstructured meshes which are widely used in many fields of Engineering. Due to the design of the GPU cards, structured meshes are better suited to work with than unstructured meshes. In order to overcome this situation, some strategies are proposed and analyzed in terms of computational gain, by means of introducing certain ordering on the unstructured meshes. The necessity of performing the simulations using unstructured instead of structured meshes is also justified by means of some test cases with analytical solution.

A large time step 1D upwind explicit scheme (CFL>1): Application to shallow water equations

It is possible to relax the Courant-Friedrichs-Lewy condition over the time step when using explicit schemes. This method, proposed by Leveque, provides accurate and correct solutions of non-sonic shocks. Rarefactions need some adjustments which are explored in the present work with scalar equation and systems of equations. The non-conservative terms that appear in systems of conservation laws introduce an extra difficulty in practical application. The way to deal with source terms is incorporated into the proposed procedure. The boundary treatment is analysed and a reflection wave technique is considered. In presence of strong discontinuities or important source terms, a strategy is proposed to control the stability of the method allowing the largest time step possible. The performance of the above scheme is evaluated to solve the homogeneous shallow water equations and the shallow water equations with source terms.

A 2D extension of a Large Time Step explicit scheme ( CFL 1 ) for unsteady problems with wet/dry boundaries

A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data.

GPU implementation of the 2D shallow water equations for the simulation of rainfall/runoff events

Hydrological processes that occur in catchments usually require large space resolution over long periods of time. The advance on numerical methods as well as the increasing power of computation are making possible the physically based simulation of these phenomena. In particular, the 2D shallow water equations can be used to provide distributions of water depth and velocity fields. The necessity of spatial resolution involves the use of a large number of elements hence increasing the computational time when simulating realistic scenarios for a long time period. This work deals with an efficient GPU implementation of the 2D shallow water equations on unstructured meshes analysing the influence of the mesh resolution both on the computational performance and the quality of the results to simulate a rainfall/runoff event. The numerical method to solve them has been developed and compared following three programming approaches: the sequential implementation and its adaptation to the multi-thread and many-core architectures. The particular detail of the influence of the mesh ordering when using unstructured triangular meshes is paid attention in this work to find the best strategy to further reduce the computational time in the context of GPU simulation. The resulting approach is efficient and can become very useful in environmental simulation of hydrological processes.

Reconstruction of 2D river beds by appropriate interpolation of 1D cross-sectional information for flood simulation

The 2D numerical simulation of river flow requires a large amount of topographic data to build an accurate Digital Terrain Model which must cover the main river channel and the area likely to be flooded. DTMs for large floodplains are often generated by LiDAR flights. However, it is often impossible to obtain LiDAR data of permanently inundated river beds. These areas are often surveyed and discrete cross-sections of the river channel are obtained. This work presents an algorithm to generate the missing information for the areas between cross-sections. The algorithm allows to generate a river bed which preserves important morphological features such as meanders and thalweg trajectory. Two benchmark cases are studied: a synthetic river-floodplain system and a real case application on a reach of the Ebro river in Spain. The cases are analyzed from a geometry and hydrodynamics perspective by performing 2D simulations with good results. This work describes an algorithm designed to reconstruct 2D river beds from 1D cross-section data.The algorithm is designed to interpolate the trajectory of the channel from the cross-section data, as well as the elevation.Tests show that the algorithm is well suited for 2D river bed reconstruction and allows to obtain good hydrodynamic simulations.

A Riemann coupled edge (RCE) 1D–2D finite volume inundation and solute transport model

A novel 1D–2D shallow water model based on the resolution of the Riemann problem at the coupled grid edges is presented in this work. Both the 1D and the 2D shallow water models are implemented in a finite volume framework using approximate Roe’s solvers that are able to deal correctly with wet/dry fronts. After an appropriate geometric link between the models, it is possible to define local Riemann problems at each coupled interface and estimate the contributions that update the cell solutions from the interfaces. The solute transport equation is also incorporated into the proposed procedure. The numerical results achieved by the 1D–2D coupled model are compared against a complete 2D model, which is considered the reference solution. The computational time is also examined.

Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations

ABSTRACT The shallow water equations have been extensively studied and used to model unsteady open channel flows in different applications. They belong to the category of hyperbolic partial differential equations and their treatment has recently been benefited from many numerical contributions leading to robust, accurate and well-balanced solutions. The correct formulation of external and internal boundary conditions is required to achieve a useful model in practical application. Control of internal boundary conditions may be useful in water distribution facilities. Therefore, development of a control strategy based on the fully dynamical mathematical model becomes attractive and justified. This work is devoted to the implementation of an adjoint based sensitivity analysis for the control of sluice gates in open-channel flow, formulated as internal boundary conditions. This is one of the most complex tasks in multiple regulated water delivery situations. Based on gradient method optimizers, the control of the whole channel to satisfy different requirements at several points of the channel is discussed. One of the achievements in this work is that the whole optimization process is performed two orders of magnitude faster than in real time. Moreover, the numerical results show this promising technique is a feasible way to obtain a robust and efficient control method.

EFFICIENT TWO-DIMENSIONAL SIMULATION MODELS FOR HYDRAULIC AND MORPHODYNAMIC TRANSIENTS

Recent advances in the simulation of shallow flows over mobile bed have shown that accurate and stable results in realistic problems can be provided if an appropriate coupling between the shallow water equations (SWE) and the Exner equation is performed. In this way the computational cost may become unaffordable in situations involving large time and space scales. Therefore, for restoring the numerical efficiency, the coupling technique is simplified, not decreasing the number of waves involved in the Riemann problem but simplifying their definitions. The effects of the approximations made are tested against experimental data which include transient problems over erodible bed. The simplified model is formulated under a general framework able to insert any desirable discharge solid load formula. Also, the movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the understanding and predictions of such landslides. The main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved. However, recent advances in massive parallelization techniques for 2D hydraulic models are able to reduce computer times by orders of magnitude making 2D applications competitive and practical for operational flood prediction in large river reaches. Moreover, high performance code development can take advantage of general purpose and inexpensive Graphical Processing Units (GPU), allowing to run 2D simulations more than 100 times faster than old generation 2D codes, in some cases.