We present a model for water flow at the base of a glacier implemented with the Elmer/Ice Open-Source Finite-Element Software. The model describes subglacial water flow in connection with the emptying of basal water bodies and the subglacial propagation of glacial outburst flood (jökulhlaup) fronts using a visco-elastic model for the overlying glacier combined with a turbulent thin-sheet model for water flow. The visco-elastic model is based on Maxwell-elements1 combining linear elasticity with the non-linear viscous behaviour described by Glen's ice-flow law, and, by introducing a pressure variable, allowing for incompressibility of the material. The dynamics of the subglacial ice–water interface is implemented as fluid–structure interaction (FSI), utilizing artificial compressibility. The coupled visco-elastic, thin-sheet model aims to represent the propagation of rapidly- and slowly-rising subglacial floods2, many of which are inferred from remote-sensing and in-situ observations to involve lifting of the glacier from its sole over large areas3. Dynamically similar subglacial ice–water interactions may be involved in widespread, propagating ice-velocity and surface-elevation disturbances that have been observed by remote sensing during subglacial drainage events in Greenland4 and Antarctica5, indicating that the dynamics of jökulhlaups may have wider implications for glacier dynamics in general. We will demonstrate the coupled model with simple synthetic examples. The visco-elastic model can simulate the observed geometry of ice-surface depressions formed by the collapse of basal water cupolas and conduits, for which we present simulation results with comparison to observed ice-surface depressions at Vatnajökull ice cap, Iceland.References1Zwinger, T., Nield, G. A., Ruokolainen, J., and King, M. A.: A new open-source viscoelastic solid earth deformation module implemented in Elmer (v8.4), Geosci. Model Dev., 13, 1155–1164 (2020).2 Jóhannesson, T. Propagation of a subglacial flood wave during the initiation of a jökulhlaup. Hydrol. Sci. J., 47, 417–434 (2002).3 Magnússon, E., & 13 others. New insights into the development of slowly rising jökulhlaups from the Grímsvötn subglacial lake, Iceland, deduced from ICEYE SAR images and in-situ observations. EGU General Assembly 2024, EGU24-18204, https://doi.org/10.5194/egusphere-egu24-18204.4 Maier, N., Andersen, J.K., Mouginot, J., Gimbert, F., & Gagliardini, O. Wintertime supraglacial lake drainage cascade triggers large-scale ice flow response in Greenland. Geophys. Res. Lett., 50(4), p.e2022GL10 (2023).5Neckel, N., Franke, S., Helm, V., Drews, R., & Jansen, D. Evidence of cascading subglacial water flow at Jutulstraumen Glacier (Antarctica) derived from Sentinel-1 and ICESat-2 measurements. Geophys. Res. Lett., 48(20), p.e2021GL094472 (2021).

Within the modelling framework of Elmer/Ice we have existing model components to compute the thermo-mechanical ice flow problem, using a full-stress approach as well as several model approaches for the bedrock hydrology, for instance the Glacier Drainage System model (GlaDS - Werder et al., 2013). Further, a thermodynamically consistent groundwater model including freezing (permafrost) and thawing of the pore-water and the stress-induced deformation of the rock skeleton is implemented in Elmer. The real challenge lies within coupling those three components with mutual feedback, both, in mechanical and thermal aspects that mutually depend on each other, e.g. through a temperature and water-pressure dependent sliding law. The fact that all equations are implemented in the same Finite Element framework enables a consistent coupling of the equations solved on different domains (ice, water-sheet and sediment), in case of weakly coupling being able to use the residual to transfer loads. Along the lines of a synthetic glacier setup, we highlight the workflow of such a coupled simulation and point out the challenges of such a highly complex process model.

This paper concerns a numerical stabilization method for free-surface ice flow called the free-surface stabilization algorithm (FSSA). In the current study, the FSSA is implemented into the numerical ice-flow software Elmer/Ice and tested on synthetic two-dimensional (2D) glaciers, as well as on the real-world glacier of Midtre Lovénbreen, Svalbard. For the synthetic 2D cases it is found that the FSSA method increases the largest stable time-step size at least by a factor of 5 for the case of a gently sloping ice surface (∼ 3°) and by at least a factor of 2 for cases of moderately to steeply inclined surfaces (∼ 6° to 12°) on a fine mesh. Compared with other means of stabilization, the FSSA is the only one in this study that increases largest stable time-step sizes when used alone. Furthermore, the FSSA method increases the overall accuracy for all surface slopes. The largest stable time-step size is found to be smallest for the case of a low sloping surface, despite having overall smaller velocities. For an Arctic-type glacier, Midtre Lovénbreen, the FSSA method doubles the largest stable time-step size; however, the accuracy is in this case slightly lowered in the deeper parts of the glacier, while it increases near edges. The implication is that the non-FSSA method might be more accurate at predicting glacier thinning, while the FSSA method is more suitable for predicting future glacier extent. A possible application of the larger time-step sizes allowed for by the FSSA is for spin-up simulations, where relatively fast-changing climate data can be incorporated on short timescales, while the slow-changing velocity field is updated over larger timescales.

A robust open-source cloud-based workflow is developed for finite element (FE) data generation for active learning (AL) -based surrogate modelling.Special attention is paid to making the FE solution procedure as robust and fast as possible without human intervention by, e.g., implementing special convergence criteria, reliable parallel computation, and variable timestep length.In AL, a surrogate model automatically improves itself by iteratively querying more FE data.Using AL and large datasets generated with parallelised cloud FE simulations, we develop a surrogate model to rapidly predict induction machine steady-state torque, torque ripple, total losses, and current harmonic distortion, as a function of motor frequency, voltage, and slip.Results show that AL performs better than grid sampling and on average works as well as random sampling, but with some outputs, the results vary less with AL.In addition, accurate ripple estimation requires a much larger training dataset than the other variables.

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the unstabilized mixed mortar method. For simplicity, both methods use a Lagrange multiplier defined on a trace mesh inherited from one side of the interface only. We derive a quasi-optimality estimate for the stabilized method and present the stability criteria of the mixed P1−P1 approximation. Our numerical results demonstrate the stability and the convergence of the methods for tie contact problems. Moreover, the results show that the mixed method can be successfully extended to three dimensional problems.

While surfaces are known to have a limited impact on the mechanical properties of crystalline materials at the macroscopic scale, they play a key role at small-scale behaving alternatively as sources or sinks of various plastic deformation processes. In this study, we present a new tool called El-Numodis that relies on the superposition method to couple the discrete dislocation dynamics code Numodis to Elmer, an open-source finite-element-modeling tool. After few years of development, El-Numodis allows now for the simulation of small-scale object deformation and mechanical properties based on a large set of surface-related processes including stress-free boundaries, mirrored dislocations and a Monte-Carlo based dislocation nucleation mechanism. Here we present the main features of the code as well as numerical test-cases and benchmarks going from classical boundary value problems to tensile tests on model thin film.

<p>Glacier outburst floods, or <em>jökulhlaups</em>, from subglacial geothermal areas, marginal lakes and subglacial volcanic eruptions are common in Iceland and they pose a substantial hazard to settled areas as well as to roads, communication lines and other infrastructure near glaciers. Jökulhlaups have attracted increasing attention in recent years in many glacier areas because of an increased frequency due to the formation of terminus and marginal lakes in connection with global warming and the associated glacier downwasting. Jökulhlaups can be categorized into two groups, slowly and rapidly rising, with marked differences in the flood hydrographs. Slowly-rising jökulhlaups are traditionally explained by the theory of Nye (1976) through a conduit-melt–discharge feedback mechanism. The initial subglacial propagation and the development of the flood hydrograph of rapidly-rising jökulhlaups is, on the other hand, not quantitatively understood. We present observations of glacier outburst floods from W-Vatnajökull in Iceland that may be interpreted in terms of a conceptual theory for such floods as a pressure wave in the basal hydraulic system that propagates downglacier and creates the initial flood path by lifting the glacier from its sole. This theory is being implemented as a numerical model for rapidly-rising jökulhlaups in the Elmer/Ice Open-Source Finite-Element Software. The model describes the subglacial propagation of the jökulhlaup front using visco-elastic plate dynamics for the overlying glacier ice combined with a turbulent sheet model for the subglacial water flood. The evolution of the subglacial flooded area is simulated numerically through the solution of a contact problem that represents the lifting of the ice from the underlying glacier bed where the subglacial water pressure exceeds the normal stress in the ice at the sole of the glacier. We hence can identify 4 crucial components of the model: 1) A visco-elastic ice-deformation model, 2) a two-dimensional pressurized water-sheet model based on Manning’s law for turbulent friction in water flow, 3) the solution of a contact problem induced by hydraulic jacking of the glacier, and 4) the consistent (in terms of the spatial stress distribution) solution of the fluid–structure interaction between the ice and the water-sheet. We present and discuss these different aspects in terms of their numerical implementation in Elmer/Ice. The aim of the model is to explain the speed of propagation of the subglacial flood front at the beginning of the flood as well as the time-dependent flood hydrograph after the flood bursts out from under the glacier at the ice margin.</p>

In order to get detailed information about deformations of structures efficiently, it may be necessary to use finite element models which combine three-dimensional discretizations of solidswith approximations of two-dimensional models for shells. Here we show how the idea of conjugate approximations can be used as a means to obtain a formulation of mixed-dimensional coupling between shells and solids. Our method is consistent with respect to the principle of virtual workand does not depend on additional computational parameters, an augmentation of a potential-energy functional by introducing new unknowns, or computations over auxiliary meshes.

Intermetallics such as Ti3Au are characterised by improved mechanical properties and reduced susceptibility to corrosion. This study extensively blends the techniques of process simulation by finite element analysis, light microscopy, scanning electron microscopy, energy dispersive spectroscopy and structural roentgenography analysis to investigate the interfacial intermetallics (IMC) in Au-Ti system. Ti was electrochemically coated with a micrometric layer of gold and then laser-treated in a wide range of parameters. Variability included both the laser beam power and the beam feed rate. The experimental results confirm that the formation of an intermetallic Ti3Au phase is possible. Finite element method was employed to numerically estimate the transient temperature values at the Au-Ti interface during laser treatment. At laser power 100 W and scan speed of 1.5 mm/s, the interfacial temperature reached a magnitude larger than the melting point of Ti for a duration less than 5.0 ms. The decrease of scan speed to 1.0 mm/s for constant P, increased this duration up to 97.0 ms where both provided sufficient energy for convection-based reaction at the interface. Through nanoscale molecular dynamics simulation, it has been revealed that during nanoindentation, Ti and Au atoms of Ti3Au IMC exert a larger resistance force to the indenter as compared to the atoms of pure Ti material. The IMC material not only offers a more robust mechanical response during indentation but also exhibits superiority over pure Ti material in a corrosion test. (c) 2023 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

The paper proposes a 3D extension of the linear tensor model of magnetic permeability for axially anisotropic materials. In the proposed model, all phases of a magnetization process are considered: linear magnetization, magnetization rotation, and magnetic saturation. The model of the magnetization rotation process is based on the analyses of both anisotropic energy and magnetostatic energy, which directly connect the proposed description with physical phenomena occurring during a magnetization process. The proposed model was validated on the base of previously presented experimental characteristics. The presented extension of the tensor description of magnetic permeability enables the modelling of inductive devices with cores made of anisotropic magnetic materials and the modelling of magnetic cores subjected to mechanical stresses. It is especially suitable for finite element modelling of the devices working in a magnetic saturation state, such as fluxgate sensors.

Ice mass loss from Antarctic Ice Sheet is increasing, accelerating its contribution to global sea level rise. In the Amundsen Sea sector, recent observations of rapid ice-shelf thinning and grounding line retreat have been attributed to increased basal melting driven by inflows of warm Circumpolar Deep Water. However, recent studies have shown that basal melting alone might not be sufficient to explain the recent acceleration, retreat and thinning of the outlet glaciers in the sector.As part of the European Horizon 2020 research project PROTECT ­— that assesses and projects changes in the land-based cryosphere to produce robust projections of SLR — we conduct numerical simulations to determine the role of damage on changes observed over the last two decades in the Amundsen Sea Sector. More particularly, we use a Stokes flow formulation combined with a Continuum Damage Mechanics model of the open-source ice flow model Elmer/Ice to simulate the ice flow evolution. We initialize our ice sheet model with data assimilation methods using 1996 observations of surface velocities as well as a corrected geometry based on the current ice-sheet geometry and the ice thickness rates of change observed over the past 20 years. From this initial state, we run forward simulations over 20 years with and without damage mechanics, and compare the model evolution to observed surface velocities and ice thickness rates of change, as well as observations of grounding line positions. Our results shed light on the importance of damage in the evolution of the region, in particular an acceleration of several hundred meters per year due to the decreasing buttressing effect of the ice shelves triggered by the increasing damage.

In recent years, subglacial hydrological models as well as till deformation models have been coupled to ice-flow models in order to determine mechanical basal conditions underneath ice sheets and glaciers. These models, nevertheless, often ignore the thermo-dynamical aspects, in particular, not including the influence of permafrost in proximity to or underneath glaciers. Here we present a thermo-mechanically coupled ice-sheet bedrock model. The latter includes components of saturated aquifer water transport, soil deformation, salinity transport and – most important – energy balance including phase change of the solvent. Using synthetic flow-line setups we present studies of ice-sheet fronts, advancing either over existing permafrost or largely unfrozen soils. We investigate the heat- and meltwater-transfer between the ice-body and its substrate and discuss their impact on ice-dynamics. As the results suggest that in certain situations the water balance further demands the existence of a hydrological system between ice and bedrock, we currently work to include this third model component in form of a subglacial hydrological model. All model components are implemented in the Finite Element software Elmer, which renders their mutual coupling relatively easy, yet, numerically demanding.

We introduce a stabilized mortar method for linear elasticity and compare it to the standard mixed mortar method without stabilization. We present the stability criteria of the lowest order mixed approximation and investigate its use for tie contact problems. Our numerical results demonstrate the stability and the convergence of the methods. Moreover, the results show that the low order mixed method can be successfully extended to three dimensions.

Microwave technology is widely used in different areas of advanced industry when energy must be provided to water-containing and other materials. The main barrier in the development of microwave devices is the possibility of efficient design by modelling a microwave system in a resonant state. For technical systems, the finite element method is widely used. However, the convergence process in the microwave finite element solver is sophisticated. The process itself and the influence of mesh granularity on the accuracy of modelling of microwave chambers in resonant states have not been investigated previously. The present paper aims to fill this gap. The resonance conditions of a microwave chamber were tested from the point of view of spatial resolution of the tetrahedral mesh used for open-source ELMER FEM software. The presented results experimentally determine the limits of accuracy of the geometry of microwave resonant chamber finite element method-based models. The determined values of microwave resonant chamber dimension tolerances should be considered for both open-source and commercial software for microwave modelling.

Magnetoelastic force sensors exhibit high sensitivity and robustness. One commonly used configuration of force sensor with a ring-shaped core was presented by Mohri at al. In this configuration force is applied in the direction of a diameter of the core. However, due to inhomogeneous distribution of stresses, model of such sensor has not been presented yet. This paper is filling the gap presenting a new method of modelling the magnetoelastic effect, which is especially suitable for the finite element method. The presented implementation of proposed model is in good agreement with experimental data and creates new possibilities of modelling other devices utilizing magnetoelastic effect.

A data-driven approach combining together the experimental laser soldering, finite element analysis and machine learning, has been utilized to predict the morphology of interfacial intermetallic compound (IMC) in Sn-xAg-yCu/Cu (SAC/Cu) system. Six types of SAC solders with varying weight proportion of Ag and Cu, have been processed with fiber laser at different magnitudes of power (30−50 W) and scan speed (10−240 mm/min), and the resultant IMC morphologies characterized through scanning electron microscope are categorized as prismatic and scalloped ones. For the different alloy composition and laser parameters, finite element method (FEM) is employed to compute the transient distribution of temperature at the interface of solder and substrates. The FEM-generated datasets are supplied to a neural network that predicts the IMC morphology through the quantified values of temperature dependent Jackson parameter (αJ). The numerical value of αJ predicted from neural network is validated with experimental IMC morphologies. The critical scan speed for the morphology transition between prismatic and scalloped IMC is estimated for each solder composition at a given power. Sn-0.7Cu having the largest critical scan speed at 30 W and Sn-3.5Ag alloy having the largest critical scan speed at input power values of 40 W and 50 W, thus possessing the greatest likelihood of forming prismatic interfacial IMC during laser soldering, can be inferred as most suitable SAC solders in applications exposed to shear loads.

We provide research findings on the physics of aerosol and droplet dispersion relevant to the hypothesized aerosol transmission of SARS-CoV-2 during the current pandemic. We utilize physics-based modeling at different levels of complexity, along with previous literature on coronaviruses, to investigate the possibility of airborne transmission. The previous literature, our 0D-3D simulations by various physics-based models, and theoretical calculations, indicate that the typical size range of speech and cough originated droplets (d⩽20μm) allows lingering in the air for O(1h) so that they could be inhaled. Consistent with the previous literature, numerical evidence on the rapid drying process of even large droplets, up to sizes O(100μm), into droplet nuclei/aerosols is provided. Based on the literature and the public media sources, we provide evidence that the individuals, who have been tested positive on COVID-19, could have been exposed to aerosols/droplet nuclei by inhaling them in significant numbers e.g. O(100). By 3D scale-resolving computational fluid dynamics (CFD) simulations, we give various examples on the transport and dilution of aerosols (d⩽20μm) over distances O(10m) in generic environments. We study susceptible and infected individuals in generic public places by Monte-Carlo modelling. The developed model takes into account the locally varying aerosol concentration levels which the susceptible accumulate via inhalation. The introduced concept, ’exposure time’ to virus containing aerosols is proposed to complement the traditional ’safety distance’ thinking. We show that the exposure time to inhale O(100) aerosols could range from O(1s) to O(1min) or even to O(1h) depending on the situation. The Monte-Carlo simulations, along with the theory, provide clear quantitative insight to the exposure time in different public indoor environments.

This paper presents the efficiency analysis of magnetic flux concentrator attached to the core of fluxgate sensor made of amorphous alloy ribbon. Simulations were carried out using open-source software toolchain covering Netgen, Elmer FEM, and ParaView. The results indicate that the increase of the length of the core significantly reduces the demagnetization factor, which increases the sensitivity of fluxgate sensor. However, the use of magnetic flux concentrator does not lead to significant increase of sensitivity of fluxgate sensor with core made of thin layer magnetic material.

Iceberg calving accounts for between 30 % and 60 % of net mass loss from the Greenland Ice Sheet, which has intensified and is now the single largest contributor to global sea level rise in the cryosphere. Changes to calving rates and the dynamics of calving glaciers represent a significant uncertainty in projections of future sea level rise. A growing body of observational evidence suggests that calving glaciers respond rapidly to regional environmental change, but predictive capacity is limited by the lack of suitable models capable of simulating calving mechanisms realistically. Here, we use a 3-D full-Stokes calving model to investigate the environmental sensitivity of Store Glacier, a large outlet glacier in West Greenland. We focus on two environmental processes: undercutting by submarine melting and buttressing by ice mélange, and our results indicate that Store Glacier is likely to be able to withstand moderate warming perturbations in which the former is increased by 50 % and the latter reduced by 50 %. However, severe perturbation with a doubling of submarine melt rates or a complete loss of ice mélange destabilises the calving front in our model runs. Furthermore, our analysis reveals that stress and fracture patterns at Store's terminus are complex and varied, primarily due to the influence of basal topography. Calving style and environmental sensitivity vary greatly, with propagation of surface crevasses significantly influencing iceberg production in the northern side, whereas basal crevasses dominate in the south. Any future retreat is likely to be initiated in the southern side by a combination of increased submarine melt rates in summer and reduced mélange strength in winter. The lateral variability, as well as the importance of rotational and bending forces at the terminus, underlines the importance of using the 3-D full-Stokes stress solution when modelling Greenland's calving glaciers.

The paper “Sensitivity of calving glaciers to ice-ocean interactions under climate change: New insights from a 3D full-Stokes model” by Joe Todd, Poul Christoffersen, Thomas Zwinger, Peter Råback, and Douglas Benn investigates the response of Store Glacier’s ice front position to various forcings using a high-resolution full Stokes model. They examine the effect of an increase in undercutting by submarine melting, the effect of a concentrated vs distributed melt rates at the calving face, and a reduction in the backstress exerted by ice mélange. Overall, the authors find that Store is stable for a wide range of conditions, but starts to retreat dramatically for the strongest scenarios.