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Abstract. LISFLOOD-FP 8.0 includes second-order discontinuous Galerkin (DG2) and first-order finite-volume (FV1) solvers of the two-dimensional shallow-water equations for modelling a wide range of flows, including rapidly propagating, supercritical flows, shock waves or flows over very smooth surfaces. The solvers are parallelised on multi-core CPU and Nvidia GPU architectures and run existing LISFLOOD-FP modelling scenarios without modification. These new, fully two-dimensional solvers are available alongside the existing local inertia solver (called ACC), which is optimised for multi-core CPUs and integrates with the LISFLOOD-FP sub-grid channel model. The predictive capabilities and computational scalability of the new DG2 and FV1 solvers are studied for two Environment Agency benchmark tests and a real-world fluvial flood simulation driven by rainfall across a 2500 km2 catchment. DG2's second-order-accurate, piecewise-planar representation of topography and flow variables enables predictions on coarse grids that are competitive with FV1 and ACC predictions on 2–4 times finer grids, particularly where river channels are wider than half the grid spacing. Despite the simplified formulation of the local inertia solver, ACC is shown to be spatially second-order-accurate and yields predictions that are close to DG2. The DG2-CPU and FV1-CPU solvers achieve near-optimal scalability up to 16 CPU cores and achieve greater efficiency on grids with fewer than 0.1 million elements. The DG2-GPU and FV1-GPU solvers are most efficient on grids with more than 1 million elements, where the GPU solvers are 2.5–4 times faster than the corresponding 16-core CPU solvers. LISFLOOD-FP 8.0 therefore marks a new step towards operational DG2 flood inundation modelling at the catchment scale. LISFLOOD-FP 8.0 is freely available under the GPL v3 license, with additional documentation and case studies at https://www.seamlesswave.com/LISFLOOD8.0 (last access: 2 June 2021).

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SUMMARYThe present work addresses the numerical prediction of discontinuous shallow water flows by the application of a second-order Runge-Kutta discontinuous Galerkin scheme (RKDG2). The unsteady flow of water in a one-dimensional approach is described by the Saint Venant's model which incorporates source terms in practical applications. Therefore, the RKDG2 scheme is reformulated with a simple way to integrate source terms. Further, an adequate boundary conditions handling, by the theory of characteristics, was overviewed to be adapted to the external points of the mesh, as well as to some points of local invalidity of the Saint Venant's model. To validate the proposed technique, steady and transient test problems (all having a reference solution) were considered and computed by means of the overall method. The results were illustrated jointly with the reference solution and the results carried out by a traditional second-order finite volume (FV2) scheme implemented with the same techniques as the RKDG2. The proposed method has proven its practical consideration when solving discontinuous shallow water flow involving: non-prismatic channels, various cross-sections, smoothly varying bed topography and internal boundary conditions.

SUMMARYDiscontinuous Galerkin (DG) finite element methods have salient features that are mainly highlighted by their locality, their easiness in balancing the flux and source term gradients and their component-wise structure. In the light of this, this paper aims to provide insights into the well-balancing property of a second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method. For this purpose, a Godunov-type RKDG2 method is presented for solving the shallow water equations. The scheme is based on local DG linear approximations and does not entail any special treatment of the source terms in order to achieve well-balanced numerical results. The performance of the present RKDG2 scheme in reproducing conserved solutions for both free surface and discharge over strongly irregular topography is demonstrated by applying to several hydraulic benchmarks. Meanwhile, the effects of different slope limiting procedures on the well-balancing property are investigated and discussed. This work may provide useful guidelines for developing a well-balanced RKDG2 numerical scheme for shallow water flow simulation.

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