A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations

© 2018 The Authors Discretisation of the friction terms to ensure numerical stability and accuracy remains to be challenging for the development of robust numerical schemes to solve the shallow water equations (SWEs), particularly for applications involving very shallow flows (e.g. overland flows and wet/dry fronts) over complex domain topography. The key challenge is to ensure relaxation of the flow towards an equilibrium state characterised by the balance between friction and gravity in a computationally efficient way. To overcome this numerical challenge, this paper proposes a novel approach for discretising the friction source terms in the SWEs in the context of an explicit finite volume method. The overall numerical scheme adopts the HLLC Riemann solver and surface reconstruction method (SRM) to explicitly discretise the flux and bed slope source terms. Whilst a fully implicit scheme is used to handle the friction source terms, solution to the implicit formulation is analytically derived to explicitly update the flow variables. Compared with the existing approaches, the proposed scheme effectively resolves the issue associated with stiff relaxation without necessity to use an iteration method and it supports efficient simulation using time steps controlled only by the Courant–Friedrichs–Levy (CFL) condition. The current friction term discretisation scheme is not coupled with flux and bed slope calculation and therefore may be readily implemented in any other explicit finite volume SWE models. After being successfully validated against two benchmark tests with analytical solutions, the resulting new SWE model is applied to reproduce a rainfall-flooding event in the Upper Lee catchment in the UK

A new depth-averaged model for flow-like landslides over complex terrains with curvatures and steep slopes

Flow-like landslides are one of the most catastrophic types of natural hazards due to their high velocity and long travel distance. They travel like fluid after initiation and mainly fall into the ‘flow’ movement type in the updated Varnes classification (Hungr et al., 2014). In recent years, depth-averaged models have been widely reported to predict the velocity and run-out distance of flow-like landslides. However, most of the existing depth-averaged models present different shortcomings for application to real-world simulations. This paper presents a novel depth-averaged model featured with a set of new governing equations derived in a mathematically rigorous way based on the shallow flow assumption and Mohr-Coulomb rheology. Particularly, the new mathematical formulation takes into account the effects of vertical acceleration and curvature effects caused by complex terrain topographies. The model is derived on a global Cartesian coordinate system so that it is easy to apply in real-world applications. A Godunov-type finite volume method is implemented to numerically solve these new governing equations, together with a novel scheme proposed to discretise the friction source terms. The hydrostatic reconstruction approach is implemented and improved in the context of the new governing equations, providing well-balanced and non-negative numerical solutions for mass flows over complex domain topographies. The model is validated against several test cases, including a field-scale flow-like landslide. Satisfactory results are obtained, demonstrating the model's improved simulation capability and potential for wider applications

A novel 1D-2D coupled model for hydrodynamic simulation of flows in drainage networks

Drainage network modelling is often an essential component in urban flood prediction and risk assessment. Drainage network models most commonly use different numerical procedures to handle flows in pipes and junctions. Numerous numerical schemes and models of different levels of complexity have been developed and reported to predict flows in pipes. However, calculation of the flow conditions in junctions has received much less attention and has been traditionally achieved by solving only the continuity equation. This method is easy to implement but it neglects the momentum exchange in the junctions and cannot provide sufficient boundary conditions for the pipe calculation. In this work, a novel numerical scheme based on the finite volume solution to the two-dimensional (2D) shallow water equations (SWEs) is proposed to calculate flow dynamics in junctions, which directly takes into account both mass and momentum conservation and removes the necessity of implementing complicated boundary settings for pipe calculations. This new junction simulation method is then coupled with the widely used two-component pressure approach (TPA) for the pipe flow calculation, leading to a new integrated drainage network model. The new 1D-2D coupled drainage network model is validated against an experimental and several idealised test cases to demonstrate its potential for efficient and stable simulation of flow dynamics in drainage networks.<br

New prospects for computational hydraulics by leveraging high-performance heterogeneous computing techniques

In the last two decades, computational hydraulics has undergone a rapid development following the advancement of data acquisition and computing technologies. Using a finite-volume Godunov-type hydrodynamic model, this work demonstrates the promise of modern high-performance computing technology to achieve real-time flood modeling at a regional scale. The software is implemented for high-performance heterogeneous computing using the OpenCL programming framework, and developed to support simulations across multiple GPUs using a domain decomposition technique and across multiple systems through an efficient implementation of the Message Passing Interface (MPI) standard. The software is applied for a convective storm induced flood event in Newcastle upon Tyne, demonstrating high computational performance across a GPU cluster, and good agreement against crowd- sourced observations. Issues relating to data availability, complex urban topography and differences in drainage capacity affect results for a small number of areas

Reply to comment by Lu et al. on “An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations”

This document addresses the comments raised by Lu et al. (2017). Lu et al. (2017) proposed an alternative numerical treatment for implementing the fully implicit friction discretization in Xia et al. (2017). The method by Lu et al. (2017) is also effective, but not necessarily easier to implement or more efficient. The numerical wiggles observed by Lu et al. (2017) do not affect the overall solution accuracy of the surface reconstruction method (SRM). SRM introduces an antidiffusion effect, which may also lead to more accurate numerical predictions than hydrostatic reconstruction (HR) but may be the cause of the numerical wiggles. As suggested by Lu et al. (2017), HR may perform equally well if fine enough grids are used, which has been investigated and recognized in the literature. However, the use of refined meshes in simulations will inevitably increase computational cost and the grid sizes as suggested are too small for real-world applications

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2Haltwhistle Burn, UK

City-scale hydrodynamic modelling of urban flash floods: the issues of scale and resolution

Hydrodynamic models have been widely used in urban flood modelling. Due to the prohibitive computational cost, most of urban flood simulations have been currently carried out at low spatial resolution or in small localised domains, leading to unreliable predictions. With the recent advance in high-performance computing technologies, GPU-accelerated hydrodynamic models are now capable of performing high-resolution simulations at a city scale. This paper presents a multi-GPU hydrodynamic model applied to reproduce a flood event in a 267.4 km2 urbanised domain in Fuzhou, Fujian Province, China. At 2 m resolution, the simulation is completed in nearly real time, demonstrating the efficiency and robustness of the model for high-resolution flood modelling. The model is used to further investigate the effects of varying spatial resolution and using localised domains on the simulation results. It is recommended that urban flood simulations should be performed at resolutions higher than 5 m and localised simulations may introduce unacceptable numerical errors

A multi-scale mapping approach based on a deep learning CNN model for reconstructing high-resolution urban DEMs

The scarcity of high-resolution urban digital elevation model (DEM) datasets, particularly in certain developing countries, has posed a challenge for many water-related applications such as flood risk management. A solution to address this is to develop effective approaches to reconstruct high-resolution DEMs from their low-resolution equivalents that are more widely available. However, the current high-resolution DEM reconstruction approaches mainly focus on natural topography. Few attempts have been made for urban topography, which is typically an integration of complex artificial and natural features. This study proposed a novel multi-scale mapping approach based on convolutional neural network (CNN) to deal with the complex features of urban topography and to reconstruct high-resolution urban DEMs. The proposed multi-scale CNN model was firstly trained using urban DEMs that contained topographic features at different resolutions, and then used to reconstruct the urban DEM at a specified (high) resolution from a low-resolution equivalent. A two-level accuracy assessment approach was also designed to evaluate the performance of the proposed urban DEM reconstruction method, in terms of numerical accuracy and morphological accuracy. The proposed DEM reconstruction approach was applied to a 121 km2 urbanized area in London, United Kingdom. Compared with other commonly used methods, the current CNN-based approach produced superior results, providing a cost-effective innovative method to acquire high-resolution DEMs in other data-scarce regions

A full-scale fluvial flood modelling framework based on a high-performance integrated hydrodynamic modelling system (HiPIMS)

Full-scale fluvial flood modelling over large catchments has traditionally been carried out using coupled hydrological and hydraulic/hydrodynamic models. Such a traditional modelling approach is not well suited for the simulation of extreme floods induced by intense rainfall, which is usually featured with highly transient and dynamic rainfall-runoff and flooding process. This work aims to develop and demonstrate a modelling framework to predict the full-scale process of fluvial flooding from the source (rainfall) to impact (inundation) over a large catchment using a single high-performance hydrodynamic model driven by rainfall inputs. The modelling framework is applied to reproduce the flood event caused by the 2015 Storm Desmond in the 2500 km2 Eden Catchment at 5 m resolution. Without intensive model calibration, the predicted results compare well with field observations in terms of inundation extent and gauged water levels across the catchment. Sensitivity tests reveal that high-resolution grid is essential for accurate simulation of fluvial flood events using a 2D hydrodynamic model. Accelerated by multiple modern GPUs, the simulation is more than 2.5 times faster than real time although it involves 100 million computational cells inside the computational domain. This work provides a novel and promising approach to assess and forecast at real time the risk of extreme fluvial floods from intense rainfall

A new GPU-accelerated coupled discrete element and depth-averaged model for simulation of flow-like landslides

Flow-like landslides are a common type of natural hazards that may impose a great risk to people and their properties. Different models have been reported for simulating flow-like landslides, all of which possess limitations due to the underlying assumptions and simplifications. Harnessing the advantages of two types of prevailing modelling approaches, a new coupled model is developed which adopts a discrete element method (DEM) model to simulate the complex collapsing process in the source area and a depth-averaged model (DAM) to predict the predominantly convective movement in the runout and deposition zones. The coupled model is finally implemented on the NVIDIA CUDA programming platform to achieve GPU high-performance computing. Two laboratory tests are considered to validate the model and a field-scale landslide event is simulated to verify its applicability in real-world conditions. Satisfactory results confirm that the coupled model is able to reproduce the dynamic process of real-world flow-like landslides