Simulating the aftermath of Northern European Enclosure Dam (NEED) break and flooding of European coast

TL;DR

This work addresses a hypothetical Northern European Enclosure Dam (NEED) break and subsequent coastal flooding by coupling an adaptive, graph-grammar–based global Earth mesh with a nonlinear wave equation solved on a spherical coordinate system via finite elements and the generalized-$\alpha$ time integrator. The first building block introduces a CP-graph framework for Rivara long-edge refinement, enabling efficient, hanging-node–free mesh refinement on the sphere; the second builds a tsunami-like dam-break model using $\frac{\partial^2 u}{\partial t^2} - \nabla\big( g(u-h_b) \nabla u \big) = 0$ with $c^2 = g(u-h_b)$, informed by GMRT bathymetry. The simulations show a traveling flood wave at about $10\ \mathrm{km\,h^{-1}}$ that raises the dammed region by $6\ \mathrm{m}$, underscoring the need for additional coastal barriers, and the implementation demonstrates strong parallel performance (e.g., 20 iterations in under 4 seconds on 48 cores). The work provides open-source tools and workflows for global-scale tsunami risk assessment, with implications for planning and mitigation of extreme sea-level rise scenarios.

Abstract

The Northern European Enclosure Dam (NEED) is a hypothetical project to prevent flooding in European countries following the rising ocean level due to melting arctic glaciers. This project involves the construction of two large dams between Scotland and Norway, as well as England and France. The anticipated cost of this project is 250 to 500 billion euros. In this paper, we present the simulation of the aftermath of flooding on the European coastline caused by a catastrophic break of this hypothetical dam. From our simulation results, we can observe that there is a traveling wave after the accident, with a velocity of around 10 kilometers per hour, raising the sea level permanently inside the dammed region. This observation implies a need to construct additional dams or barriers protecting the northern coastline of the Netherlands and the interior of the Baltic Sea. Our simulations have been obtained using the following building blocks. First, a graph transformation model was applied to generate an adaptive mesh approximating the topography of the Earth. We employ the composition graph grammar model for breaking triangular elements in the mesh without the generation of hanging nodes. Second, the wave equation is formulated in a spherical latitude-longitude system of coordinates and solved by a high-order time integration scheme using the generalized $α$ method.

Figures (32)

• Figure 1: An exemplary two-element mesh and the corresponding CP-graph.
• Figure 2: Rivara algorithm of refinement, step by step.
• Figure 3: Production $GT1$, marking element for breaking.
• Figure 4: Production $GT2$, propagation of refinement marker.
• Figure 5: Production $GT3$, breaking of common longest edge.