ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature regimes. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties. The self-similar radial profile and the development of large-scale structures are reproduced, including the rate of entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. Coarse particles partially decouple from the gas within eddies, modifying the turbulent structure, and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the gravity. By these mechanisms, gas-particle non-equilibrium is able to influence the large-scale behavior of volcanic plumes.Comment: 29 pages, 22 figure

Ash plume properties retrieved from infrared images: a forward and inverse modeling approach

We present a coupled fluid-dynamic and electromagnetic model for volcanic ash plumes. In a forward approach, the model is able to simulate the plume dynamics from prescribed input flow conditions and generate the corresponding synthetic thermal infrared (TIR) image, allowing a comparison with field-based observations. An inversion procedure is then developed to retrieve ash plume properties from TIR images. The adopted fluid-dynamic model is based on a one-dimensional, stationary description of a self-similar (top-hat) turbulent plume, for which an asymptotic analytical solution is obtained. The electromagnetic emission/absorption model is based on the Schwarzschild's equation and on Mie's theory for disperse particles, assuming that particles are coarser than the radiation wavelength and neglecting scattering. [...] Application of the inversion procedure to an ash plume at Santiaguito volcano (Guatemala) has allowed us to retrieve the main plume input parameters, namely the initial radius $b_0$, velocity $U_0$, temperature $T_0$, gas mass ratio $n_0$, entrainment coefficient $k$ and their related uncertainty. Moreover, coupling with the electromagnetic model, we have been able to obtain a reliable estimate of the equivalent Sauter diameter $d_s$ of the total particle size distribution. The presented method is general and, in principle, can be applied to the spatial distribution of particle concentration and temperature obtained by any fluid-dynamic model, either integral or multidimensional, stationary or time-dependent, single or multiphase. The method discussed here is fast and robust, thus indicating potential for applications to real-time estimation of ash mass flux and particle size distribution, which is crucial for model-based forecasts of the volcanic ash dispersal process.Comment: 41 pages, 13 figures, submitted pape

DNS of compressible multiphase flows through the Eulerian approach

In this paper we present three multiphase flow models suitable for the study of the dynamics of compressible dispersed multiphase flows. We adopt the Eulerian approach because we focus our attention to dispersed (concentration smaller than 0.001) and small particles (the Stokes number has to be smaller than 0.2). We apply these models to the compressible ($\text{Ma} = 0.2,\,0.5$) homogeneous and isotropic decaying turbulence inside a periodic three-dimensional box ($256^3$ cells) using a numerical solver based on the OpenFOAM$^{R}$ C++ libraries. In order to validate our simulations in the single-phase case we compare the energy spectrum obtained with our code with the one computed by an eighth order scheme getting a very good result (the relative error is very small $4*10^{-4}$). Moving to the bi-phase case, initially we insert inside the box an homogeneous distribution of particles leaving unchanged the initial velocity field. Because of the centrifugal force, turbulence induce particle preferential concentration and we study the evolution of the solid-phase density. Moreover, we do an {\em a-priori} test on the new sub-grid term of the multiphase equations comparing them with the standard sub-grid scale term of the Navier-Stokes equations.Comment: 10 pages, 5 figures, preprint. Direct and Large Eddy Simulations 9, 201

IMEX_SfloW2D 1.0: a depth-averaged numerical flow model for pyroclastic avalanches

Abstract. Pyroclastic avalanches are a type of granular flow generated at active volcanoes by different mechanisms, including the collapse of steep pyroclastic deposits (e.g., scoria and ash cones), fountaining during moderately explosive eruptions, and crumbling and gravitational collapse of lava domes. They represent end-members of gravity-driven pyroclastic flows characterized by relatively small volumes (less than about 1 Mm3) and relatively thin (1–10 m) layers at high particle concentration (10–50 vol %), manifesting strong topographic control. The simulation of their dynamics and mapping of their hazards pose several different problems to researchers and practitioners, mostly due to the complex and still poorly understood rheology of the polydisperse granular mixture and to the interaction with the complex natural three-dimensional topography, which often causes rapid rheological changes. In this paper, we present IMEX_SfloW2D, a depth-averaged flow model describing the granular mixture as a single-phase granular fluid. The model is formulated in absolute Cartesian coordinates (whereby the fluid flow equations are integrated along the direction of gravity) and can be solved over a topography described by a digital elevation model. The numerical discretization and solution algorithms are formulated to allow for a robust description of wet–dry conditions (thus allowing us to accurately track the front propagation) and an implicit solution to the nonlinear friction terms. Owing to these features, the model is able to reproduce steady solutions, such as the triggering and stopping phases of the flow, without the need for empirical conditions. Benchmark cases are discussed to verify the numerical code implementation and to demonstrate the main features of the new model. A preliminary application to the simulation of the 11 February pyroclastic avalanche at the Etna volcano (Italy) is finally presented. In the present formulation, a simple semi-empirical friction model (Voellmy–Salm rheology) is implemented. However, the modular structure of the code facilitates the implementation of more specific and calibrated rheological models for pyroclastic avalanches

Book of Abstracts

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The effects of vent location, event scale and time forecasts on pyroclastic density current hazard maps at Campi Flegrei caldera (Italy)

This study presents a new method for producing long-term hazard maps for pyroclastic density currents (PDC) originating at Campi Flegrei caldera. Such method is based on a doubly stochastic approach and is able to combine the uncertainty assessments on the spatial location of the volcanic vent, the size of the flow and the expected time of such an event. The results are obtained by using a Monte Carlo approach and adopting a simplified invasion model based on the box model integral approximation. Temporal assessments are modeled through a Cox-type process including self-excitement effects, based on the eruptive record of the last 15 kyr.Mean and percentilemaps of PDC invasion probability are produced, exploring their sensitivity to some sources of uncertainty and to the effects of the dependence between PDC scales and the caldera sector where they originated. Conditional maps representative of PDC originating inside limited zones of the caldera, or of PDC with a limited range of scales are also produced. Finally, the effect of assuming different time windows for the hazard estimates is explored, also including the potential occurrence of a sequence of multiple events. Assuming that the last eruption of Monte Nuovo (A.D. 1538) marked the beginning of a new epoch of activity similar to the previous ones, results of the statistical analysis indicate a mean probability of PDC invasion above 5% in the next 50 years on almost the entire caldera (with a probability peak of 25% in the central part of the caldera). In contrast, probability values reduce by a factor of about 3 if the entire eruptive record is considered over the last 15 kyr, i.e., including both eruptive epochs and quiescent periods

11th EGU Galileo Conference: Solid Earth and Geohazards in the Exascale Era Consensual Document

The 11th Galileo Conference in Barcelona (May 23-26, 2023) addressed Exascale computing challenges in geosciences. With 78 participants from 15 countries, it focused on European-based research but welcomed contributions from worldwide institutions. The conference had four sessions covering HPC applications, data workflows, computational geosciences, and EuroHPC infrastructures. It featured keynote presentations, poster sessions, and breakout sessions, including Master Classes for 22 Early Career Scientists supported by EGU. This document represents the consensus among participants, capturing outcomes from breakout sessions and acknowledging diverse opinions and approaches.The 11th Galileo Conference of the European Geosciences Union (EGU) focused on "Solid Earth and Geohazards in the Exascale Era." This abstract presents the main outcomes and conclusions from the conference breakout sessions, which aimed to provide recommendations for the future of solid earth research. The discussions highlighted the challenges and opportunities associated with high-performance computing (HPC) in solid earth sciences. The key findings include the need for collaboration between computer scientists and solid earth domain-specific scientists, the importance of portability software layers for different hardware architectures, the adoption of programming models for easier development and deployment of applications, the necessity of HPC training at all career stages, the improvement of accessibility and authentication mechanisms for European machines, and the readiness of urgent computing services for natural catastrophes. The conference also emphasized the significance of sustainable funding, software engineering best practices, and the development of modular and interoperable codes and workflows. Overall, the conference provided insights into the current status of computational solid earth research and offered recommendations for future advancements in the field.European Geosciences Union (EGU), the EuroHPC Center of Excellence for Exascale in Solid Earth (ChEESE) under Grant Agreement No 101093038 (https://cheese2.eu), and the European Union's Next Generation/PRTR Program through grant PCI2022-134973-2.Peer reviewe

The EU Center of Excellence for Exascale in Solid Earth (ChEESE): Implementation, results, and roadmap for the second phase

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