Inverse computational algorithms for flood plain dynamic modelling

Flood plain dynamic modelling remains a challenge because of the complex multi-scale data, data uncertainties and the uncertain heterogeneous flow measurements. Mathematical models based on the 2d shallow water equations are generally suitable but wetting-drying processes can be driven by small scale data features. The present study aims at deriving an accurate and robust direct solver for dynamic wet-dry fronts and a variational inverse method leading to sensitivity analyses and data assimilation processes. The numerical schemes and algorithms are assessed on academic benchmarks representing well some flood dynamic features and a real test case (Lèze river, southwestern of France). Original sensitivity maps with respect to the (friction , topography) fields are performed and discussed. Furthermore, the identification of inflow discharges (time series) or roughness coefficients defined by land covers (spatially distributed parameters) demonstrate the relevance of the approach and the algorithm efficiency. Inverse computational methods may contribute to breakthrough in flood plain modelling

Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics

This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties

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

On the assimilation of altimetric data in 1D Saint-Venant river flow models

Given altimetry measurements, the identification capability of time varying inflow discharge Qin(t) and the Strickler coefficient K (defined as a power-law in h the water depth) of the 1D river Saint-Venant model is investigated. Various altimetry satellite missions provide water level elevation measurements of wide rivers, in particular the 21 future Surface Water and Ocean Topography (SWOT) mission. An original and synthetic reading of all the available information (data, wave propagation and the Manning-Strickler’s law residual) are represented on the so-called identifiability map. The latter provides in the space-time plane a comprehensive overview of the inverse problem features. Inferences based on Variational Data Assimilation (VDA) are investigated at the limit of the data-model inversion capability : relatively short river portions, relatively infrequent observations, that is inverse problems presenting a low identifiability index . The inflow discharge Qin(t) is infered simultaneously with the varying coefficient K(h). The bed level is either given or infered from a lower complexity model. The experiments and analysis are conducted for different scenarios (SWOT-like or multi-sensors-like). The scenarios differ by the observation frequency and by the identifiability index. Sensitivity analyses with respect to the observation errors and to the first guess values demonstrate the robustness of the VDA inferences. Finally this study aiming at fusing relatively sparse altimetric data and the 1D Saint-Venant river flow model highlights the spatiotemporal resolution lower limit, also the great potential in terms of discharge inference including for a single river reach

DassFow-Shallow, Variational Data Assimilation for Shallow-Water Models: Numerical Schemes, User and Developer Guides

DassFlow is a computational software for free-surface flows includingvariational data assimilation (4D-VAR), sensitivity analysis, calibration features (adjoint method). The code version "shallow" solves shallow-water like models (Saint-Venant's type).The other version (ALE, not detailed in the present document) includes free-surface Stokes like models (low Reynolds, power-law rheology, ALE surface dynamics). All source files are written in Fortran 2003 / MPI. For more details and references, please consult DassFlow website.In the present manuscript, we describe: the equations, the compilation/execution instructions, the input / output files (user guide), the finite volume schemes, few validation test cases included in the archive, and the code structure (developer guide)

The source mechanisms of low frequency seismic events on volcanoes

Volcanoes generate a variety of seismic signals. One specific type, the so-called low frequency (LF) event, has proven to be crucial for understanding the internal dynamics of the volcanic system. While many endeavours have concentrated on the nature and cause of the seismic coda, the actual trigger mechanism of these events is still poorly understood. Several conceptual source models have been developed, ranging from magma-water interaction, stick-slip motion of magma plugs, magma flow instabilities, repeated release of gas-ash mixtures into open cracks, magma wagging, to brittle fracturing of magma. All but one trigger model, namely brittle failure of magma in the glass transition as response to the upwards movement of magma, fail to explain all observed characteristics of LF volcanic seismicity. Here, a spatially extended source, the ring fault structure, is developed to mimic the proposed source mechanism. The extended LF source is modelled as an arrangement of 8, 16 and 32 double couples (DCs) approximating a 30 m, 50 m and 70 m wide circular ring fault bounding the circumference of the volcanic conduit. Due to (partial) destructive interference, P-wave amplitudes of a ring fault structure are greatly reduced compared to single double couples and compensated linear vector dipoles (CLVDs), by 350% and 470%, respectively. It is shown here that these seismic amplitude differences may result in the underestimation of average slip and thus magma ascent rate by a factor of up to 3.5 when using an over simplified point source. To resolve the driving forces of LFs, synthetic seismograms representing both point and spatially extended sources were inverted for the apparent physical source mechanism using moment tensor inversion techniques (MTI). If original input parameters were unknown, MTI results of the ring fault would indicate a combination of 63% isotropic and 37% CLVD components. The proposed moment tensor strongly resembles that of a real CLVD case. The results of this study give evidence that slip along the conduit walls yields the same MTI results as a subhorizontal tensile crack, and the importance of knowledge about the source nature becomes eminently significant. Spatially extended source geometries describe an alternative to point dislocation sources. Additionally to the ring fault structure, this study provides a catalogue of further complex source scenarios involving new spatially extended sources, such as slip along a dike, conduit segments, two simultaneously acting ring fault structures, and helix-like flow patterns. P-wave amplitudes and waveforms vary largely with source geometry, stressing that source geometry is key for source interpretations and thus it is not sufficient to assume a point source nature of the processes involved to generated the observed seismicity

Efficient explicit finite volume schemes for the shallow water equations with solute transport

This work is concerned with the design and the implementation of efficient and novel numerical techniques in the context of the shallow water equations with solute transport, capable to improve the numerical results achieved by existing explicit approaches. When dealing with realistic applications in Hydraulic Engineering, a compromise between accuracy and computational time is usually required to simulate large temporal and spatial scales in a reasonable time. With the aim to improve the existent numerical methods in such a way to increase accuracy and reduce computational time. Three main contributions are envisaged in this work: a pressure-based source term discretization for the 1D shallow water equations, the analysis and development of a Large Time Step explicit scheme for the 1D and 2D shallow water equations with source terms and the numerical coupling between the 1D and the 2D shallow water equations in a 1D-2D coupled model. The first improvement roughly consists of exploring the pressure and bed slope source terms that appear in the 1D and 2D shallow water equations to discretize them in an intelligent way to avoid extremely reductions in the time step size. On the other hand, the implementation of a Large Time Step scheme is carried out. In order to relax the stability condition associated to explicit schemes and to allow large time step sizes, reducing consequently the numerical diffusion associated to the original explicit scheme. Finally, two 1D-2D coupled models are developed. They are demonstrated to be fully conservative and are able to approximate well the results obtained by a fully 2D model in terms of accuracy, while the computational effort is clearly reduced. All the advances are analysed by means of different test cases, including not only academic configurations but also realistic applications, in which the numerical results achieved by the new numerical techniques proposed in this work are compared with the conventional approaches

Proceedings of the XXVIIIth TELEMAC User Conference 18-19 October 2022

Hydrodynamic

Simulating High Flux Isotope Reactor Core Thermal-Hydraulics via Interdimensional Model Coupling

A coupled interdimensional model is presented for the simulation of the thermal-hydraulic characteristics of the High Flux Isotope Reactor core at Oak Ridge National Laboratory. The model consists of two domains—a solid involute fuel plate and the surrounding liquid coolant channel. The fuel plate is modeled explicitly in three-dimensions. The coolant channel is approximated as a two-dimensional slice oriented perpendicular to the fuel plate’s surface. The two dimensionally-inconsistent domains are linked to one another via interdimensional model coupling mechanisms. The coupled model is presented as a simplified alternative to a fully explicit, fully three-dimensional model. Involute geometries were constructed in SolidWorks. Derivations of the involute construction equations are presented. Geometries were then imported into COMSOL Multiphysics for simulation and modeling. Both models are described in detail so as to highlight their respective attributes—in the 3D model, the pursuit of an accurate, reliable, and complete solution; in the coupled model, the intent to simplify the modeling domain as much as possible without affecting significant alterations to the solution. The coupled model was created with the goal of permitting larger portions of the reactor core to be modeled at once without a significant sacrifice to solution integrity. As such, particular care is given to validating incorporated model simplifications. To the greatest extent possible, the decrease in solution time as well as computational cost are quantified versus the effects such gains have on the solution quality. A variant of the coupled model which sufficiently balances these three solution characteristics is presented alongside the more comprehensive 3D model for comparison and validation