scholarly journals LISFLOOD-FP 8.0: the new discontinuous Galerkin shallow-water solver for multi-core CPUs and GPUs

2021 ◽  
Vol 14 (6) ◽  
pp. 3577-3602
Author(s):  
James Shaw ◽  
Georges Kesserwani ◽  
Jeffrey Neal ◽  
Paul Bates ◽  
Mohammad Kazem Sharifian
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Channel Model ◽  
Second Order ◽  
Two Dimensional ◽  
River Channels ◽  
Catchment Scale ◽  
Wide Range ◽  
Nvidia Gpu ◽  
Flow Variables

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).

scholarly journals LISFLOOD-FP 8.0: the new discontinuous Galerkin shallow water solver for multi-core CPUs and GPUs

2020 ◽  
Author(s):  
James Shaw ◽  
Georges Kesserwani ◽  
Jeffrey Neal ◽  
Paul Bates ◽  
Mohammad Kazem Sharifian
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Second Order ◽  
River Channels ◽  
Catchment Scale ◽  
Wide Range ◽  
Inundation Modelling ◽  
Nvidia Gpu ◽  
Gpu Architectures ◽  
Flow Variables

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. Alongside the existing local inertia solver (called ACC), the new solvers are parallelised on multi-core CPU and Nvidia GPU architectures and run existing LISFLOOD-FP modelling scenarios without modification. The predictive capabilities and computational scalability of the new 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 × 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 × 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.

scholarly journals Reformulation of 2D DG2 Scheme for Shallow Water Modelling

10.29007/xlvx ◽  
2018 ◽  
Author(s):  
Janice Ayog ◽  
Georges Kesserwani
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Real World ◽  
Second Order ◽  
Shock Propagation ◽  
Linear Solution ◽  
Galerkin Scheme ◽  
Flood Modelling ◽  
Discontinuous Galerkin Scheme ◽  
Local Coefficients

This paper presents a reformulation of the 2D second-order discontinuous Galerkin scheme (2D DG2) which is more efficient and stable for realistic simulation of hydrodynamics. This modified scheme is formulated based on a local linear solution spanned by a set of local coefficients using a newly proposed cell stencil. The results show that the reformulated second-order discontinuous Galerkin scheme performs acceptably well in predicting shock propagation. The modified scheme is designed to be conservative not only for the average coefficients but also the slope coefficients, which is necessary to ensure robustness based on the well-balanced property under the lake at rest hypothesis. Our preliminary findings reveal a great potential from adopting the proposed 2D DG2 reformulation as a basis for real-world flood modelling applications.

scholarly journals A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
W. Lai ◽  
A. A. Khan
Keyword(s):  
Shock Waves ◽  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Dam Break ◽  
Two Dimensional ◽  
Simple Method ◽  
Water Flows ◽  
Shallow Water Flows

A numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify computation is adopted here. The HLL approximate Riemann solver is employed to calculate the mass and momentum flux. A slope limiting procedure that is suitable for incompressible two-dimensional flows is presented. A simple method is adapted for flow over initially dry bed. A new formulation is introduced for modeling the net pressure force and gravity terms in discontinuous Galerkin method. To validate the scheme, numerical tests are performed to model steady and unsteady shock waves. Applications include circular dam break with shock, shock waves in channel contraction, and dam break in channel with bend. Numerical results show that the scheme is accurate and efficient to model two-dimensional shallow water flows with shock waves.

scholarly journals A fast second-order shallow water scheme on two-dimensional structured grids over abrupt topography

2019 ◽  
Vol 127 ◽  
pp. 89-108 ◽  
Author(s):  
Andreas Buttinger-Kreuzhuber ◽  
Zsolt Horváth ◽  
Sebastian Noelle ◽  
Günter Blöschl ◽  
Jürgen Waser
Keyword(s):  
Shallow Water ◽  
Second Order ◽  
Two Dimensional ◽  
Structured Grids
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