Abstract

Abstract. Plume-SPH provides the first particle-based simulation of volcanic plumes. Smoothed particle hydrodynamics (SPH) has several advantages over currently used mesh-based methods in modeling of multiphase free boundary flows like volcanic plumes. This tool will provide more accurate eruption source terms to users of volcanic ash transport and dispersion models (VATDs), greatly improving volcanic ash forecasts. The accuracy of these terms is crucial for forecasts from VATDs, and the 3-D SPH model presented here will provide better numerical accuracy. As an initial effort to exploit the feasibility and advantages of SPH in volcanic plume modeling, we adopt a relatively simple physics model (3-D dusty-gas dynamic model assuming well-mixed eruption material, dynamic equilibrium and thermodynamic equilibrium between erupted material and air that entrained into the plume, and minimal effect of winds) targeted at capturing the salient features of a volcanic plume. The documented open-source code is easily obtained and extended to incorporate other models of physics of interest to the large community of researchers investigating multiphase free boundary flows of volcanic or other origins. The Plume-SPH code (https://doi.org/10.5281/zenodo. 572819) also incorporates several newly developed techniques in SPH needed to address numerical challenges in simulating multiphase compressible turbulent flow. The code should thus be also of general interest to the much larger community of researchers using and developing SPH-based tools. In particular, the SPH−ε turbulence model is used to capture mixing at unresolved scales. Heat exchange due to turbulence is calculated by a Reynolds analogy, and a corrected SPH is used to handle tensile instability and deficiency of particle distribution near the boundaries. We also developed methodology to impose velocity inlet and pressure outlet boundary conditions, both of which are scarce in traditional implementations of SPH. The core solver of our model is parallelized with the message passing interface (MPI) obtaining good weak and strong scalability using novel techniques for data management using space-filling curves (SFCs), object creation time-based indexing and hash-table-based storage schemes. These techniques are of interest to researchers engaged in developing particles in cell-type methods. The code is first verified by 1-D shock tube tests, then by comparing velocity and concentration distribution along the central axis and on the transverse cross with experimental results of JPUE (jet or plume that is ejected from a nozzle into a uniform environment). Profiles of several integrated variables are compared with those calculated by existing 3-D plume models for an eruption with the same mass eruption rate (MER) estimated for the Mt. Pinatubo eruption of 15 June 1991. Our results are consistent with existing 3-D plume models. Analysis of the plume evolution process demonstrates that this model is able to reproduce the physics of plume development.

Highlights

  • 1.1 Volcanic ash hazardsPrimary hazards associated with explosive volcanic eruptions include pyroclastic density currents, the widespread deposition of air fall tephra and the threats to aviation posed by volcanic ash in the atmosphere

  • This paper reports on a new three-dimensional (3-D) volcanic plume model designed to exploit the advantages of mesh-free methods for 3-D modeling of such plumes that involve multiphase free boundary flows

  • Several one-dimensional (1-D) volcanic plume models have been developed in the past few decades, ranging from the most basic 1-D model (Woods, 1988) which only accounts for mass conservation to more recently developed 1-D models (Bursik, 2001; Mastin, 2007; Degruyter and Bonadonna, 2012; Woodhouse et al, 2013; Devenish, 2013; de’Michieli Vitturi et al, 2015; Folch et al, 2016; Pouget et al, 2016) which tend to account for more comprehensive physics effects

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Summary

Volcanic ash hazards

Primary hazards associated with explosive volcanic eruptions include pyroclastic density currents (flows and surges), the widespread deposition of air fall tephra and the threats to aviation posed by volcanic ash in the atmosphere. Volcanic ash transport and dispersion models (VATDs) are used to forecast the location and movement of ash clouds at timescales that range from hours to days. VATDs use eruption source parameters, such as plume height, mass eruption rate, duration and the mass fraction distribution of erupted particles finer than about 4 (or 62.5 μm), which can remain in the cloud for many hours or days. Observational data for such parameters are usually unavailable in the first minutes or hours after an eruption is detected. This paper reports on a new three-dimensional (3-D) volcanic plume model designed to exploit the advantages of mesh-free methods for 3-D modeling of such plumes that involve multiphase free boundary flows

Existing plume models
Features of SPH
Our contributions
Description of the model
Governing equations
Velocity inlet
Non-slip wall boundary
Open outlet pressure boundary condition
SPH method
Fundamental principles
Artificial viscosity
Discretization of governing equations and extensibility
Time step
Tensile instability and corrected derivatives
Mass fraction update
Turbulence modeling with SPH
Turbulent heat transfer
Wall boundary condition
Eruption boundary condition
Pressure boundary condition
Parallelism and performance
Verification and validation
Simulation of JPUE
Simulation of a volcanic plume
Input parameters
Global and local variables
Findings
Conclusions
Full Text
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