A parallel code for the simulation of the transient 3D dispersal of volcanic particles produced by explosive eruptions is presented. The model transport equations, based on the multiphase flow theory, describe the atmospheric dynamics of the gas-particle mixture ejected through the volcanic crater. The numerics is based on a finite-volume discretization scheme and a pressure-based iterative non-linear solver suited to compressible multiphase flows. The code has been parallelized by adopting an ad hoc domain partitioning scheme that enforces the load balancing. An optimized communication layer has been built over the Message-Passing Interface. The code proved to be remarkably efficient on several 

high-performance platforms and makes it possible to simulate fully 3D eruptive scenarios on realistic volcano topography

Cavazzoni, C.

Erbacci, G.

Esposti Ongaro, T.

Nannipieri, L.

Neri, A.

English

A parallel code for the simulation of the transient 3D dispersal of volcanic particles produced by explosive eruptions is presented. The model transport equations, based on the multiphase ﬂow theory, describe the atmospheric dynamics of the gas-particle mixture ejected through the volcanic crater. The numerics is based on a ﬁnite-volume discretization scheme and a pressure-based iterative non-linear solver suited to compressible multiphase ﬂows. The code has been parallelized by adopting an ad hoc domain partitioning scheme that enforces the load balancing. An optimized communication layer has been built over the Message-Passing Interface. The code proved to be remarkably efficient on several high-performance platforms and makes it possible to simulate fully 3D eruptive scenarios on realistic volcano topography.Published5-82.1. TTC - Laboratorio per le reti informatiche, GRID e calcolo avanzato3.6. Fisica del vulcanismoJCR Journalreserve

Erbacci, G

Earth-prints

An application of parallel computing to the simulation of volcanic eruptions

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2009-10373-0Colloquia: CSFI 2008IL NUOVO CIMENTO Vol. 32 C, N. 2 Marzo-Aprile 2009An application of parallel computing to the simulation of volcaniceruptionsA. Neri(1), T. Esposti Ongaro(1), L. Nannipieri(1), C. Cavazzoni(2)and G. Erbacci(2)(1) Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa - Pisa, Italy(2) CINECA, Interuniversity Computing Center - Casalecchio di Reno, Bologna, Italy(ricevuto il 15 Maggio 2009; pubblicato online il 6 Agosto 2009)Summary. — A parallel code for the simulation of the transient 3D dispersal ofvolcanic particles produced by explosive eruptions is presented. The model transportequations, based on the multiphase flow theory, describe the atmospheric dynam-ics of the gas-particle mixture ejected through the volcanic crater. The numericsis based on a finite-volume discretization scheme and a pressure-based iterativenon-linear solver suited to compressible multiphase flows. The code has been paral-lelized by adopting an ad hoc domain partitioning scheme that enforces the load bal-ancing. An optimized communication layer has been built over the Message-PassingInterface. The code proved to be remarkably efficient on several high-performanceplatforms and makes it possible to simulate fully 3D eruptive scenarios on realisticvolcano topography.PACS 02.70.-c – Computational techniques; simulations.PACS 47.11.-j – Computational methods in fluid dynamics.PACS 91.40.-k – Volcanology.PACS 47.27.-i – Turbulent flows.1. – IntroductionDuring explosive eruptions, a mixture of gas and pyroclasts (volcanic particles ofvarious nature) is ejected at high velocity, pressure, and temperature from the volcanicconduit, forming a turbulent volcanic jet. When the jet has exhausted its initial thrust,depending on the efficiency of the turbulent mixing, it can either rise by positive buoyancyto form a buoyant plume or collapse under the action of gravity to form a density current(or pyroclastic flow).Modelling of these phenomena requires indeed advanced techniques for multiphaseflow, sub- and super-sonic flows, turbulence modelling, complex geometries, non-Newtonian rheology, and free-surface stratified flows. In this paper we present a newparallel code [1], named PDAC (Pyroclastic Dispersal Analysis Code), that has beenc© Societa` Italiana di Fisica 56 A. NERI, T. ESPOSTI ONGARO, L. NANNIPIERI, C. CAVAZZONI and G. ERBACCIdeveloped on the basis of the multiphase flow model of [2], and that allows to describethe dynamics of the collapse of the volcanic column and the propagation of the relatedpyroclastic flows in fully 3D conditions.2. – The physical modelThe model transport equations can be expressed by a set of generalized Navier-Stokesequations where the density of each phase is substituted by its bulk density (i.e. the micro-scopic density multiplied by the volumetric fraction) and additional terms for interphasemomentum and energy exchange are added. For the gas phase and for each species themass, momentum and enthalpy transport equations write∂∂tgρg +∇ · (gρgvg) = 0,∂∂tgρgyj +∇ · (gρgyjvg) = 0, j = H2O,CO2, air, . . . ,ρggdvgdt=∇Tg + gρgg − g∇P +n∑l=1Mgl,ρggdhgdt= −∇gqg + g dPdt +n∑l=1Igl,whereas for each particulate phase∂∂tsρs +∇ · (sρsvs) = 0, s = 1, 2, . . . , n,ρssdvsdt=∇Ts + sρsg − s∇P −Mgl +n∑l=1Msl, s = 1, 2, . . . , n,ρssdhsdt= −∇sqs − Igs, s = 1, 2, . . . , n,where  is the volumetric fraction, ρ the density, y the mass fraction of each gas compo-nent, v the velocity, T the stress tensor, h the enthalpy, g the gravity acceleration, Mthe interphase drag, P the pressure, q the heat flux, and I the interphase heat trans-fer term. d/dt respresents the total derivative. Subscripts g, s denote the gas and solidphases, respectively. They constitute a set of 5∗(n+1)+(m−1) coupled partial differen-tial equations. Gas density and momentum equations are coupled through the gas idealequation of state, the interphase exchange terms transfer momentum and energy amongthe different phases, whereas the solid density ρs is constant. For a detailed discussionof the multiphase flow model please refer to [2] and [1].3. – Numerics and parallelization strategyThe transport equations are discretized by adopting a finite-volume approach on aorthogonal, non-uniform mesh. In 2D, the mesh can represent a poloidal half-planein cylindrical coordinates or a Cartesian slice. In 3D, only the Cartesian equations aresolved. Diffusive gradients are computed by a second-order, centered scheme, whereas theconvective gradients are computed by adopting different second-order upwind methodsAN APPLICATION OF PARALLEL COMPUTING TO THE SIMULATION ETC. 71 10 100 1000processors1001000100001e+05execution time / 100 time-stepsIBM Linux Cluster (Intel Xeon 3.06 GHz - 2 ppn)IBM Linux Cluster (Intel Xeon 3.06 GHz - 1 ppn)IBM p5-575 Cluster (IBM Power5 1.9 GHz)IBM Linux Cluster (AMD Opteron 1GHz - 2 ppn)Fig. 1. – Comparison between the execution time of three different platforms as a function ofthe number of processors.(MUSCL flux reconstruction). The system of the discretized equations is then solved bya parallel SOR iterative method. The non-linear mass and momentum coupling in eachcell is solved by a pressure-based predictor-corrector method suited for compressible flows.The volcano topography is described by using the immersed boundary technique [3].The parallelization of the numerical algorithm is based on the SPMD (Single Pro-gram Multiple Data) paradigm and it is implemented through the MPI interface. Thecomputational domain is decomposed into sub-domains of nearly equal size, in order tobalance the computational load, and each processor is charged of the solution of the modelequations in one sub-domain. Three domain-decomposition criteria are implemented inPDAC through an automatic procedure that holds for any number of processors.The parallel code has been ported and tested on different modern parallel comput-ers, representative of a large part of the architectures that the supercomputing marketoffers today. These includes the IBM-Xeon Linux Cluster and the IBM p5-575 Clusteravailable at CINECA, and the IBM-Opteron Linux Cluster available at INGV Pisa. Anexemplificative plot of the execution time as a function of the number of processors isrepresented in fig. 1 for the three different platforms and a block partitioning of thedomain.4. – ApplicationsThe new 3D multiphase flow model has been applied to the simulation of columncollapse scenarios and pyroclastic flow propagation at Vesuvius [4, 5] as well as to themodelling of volcanic blasts (see [6] for an application to the Boxing Day event of theSoufriere Hills volcano, Montserrat). As an example, fig. 2 shows the flow pattern charac-terizing the collapsing regime of a volcanic column. Simulation results clearly illustratedthe unsteady and asymmetric regime of the transitional column able to effectively split8 A. NERI, T. ESPOSTI ONGARO, L. NANNIPIERI, C. CAVAZZONI and G. ERBACCIFig. 2. – (Colour on-line) 3D view of the complex flow pattern characterizing the collapse of thevolcanic column. The brown isosurface corresponds to a total volume concentration of volcanicparticles of 10−6. The red lines shown illustrate the flow streamlines followed by the innerportion of the column.the erupted mass among collapsing and convective streams. Results can also be used inthe quantification of the hazardous actions associated to these explosive phenomena aswell as to the assessment of their impact and risk for the nearby regions.∗ ∗ ∗This work was mostly supported by the EU-funded project EXPLORIS (EVR1-CT-2002-40026).REFERENCES[1] Esposti Ongaro T., Cavazzoni C., Erbacci G., Neri A. and Salvetti M. V., ParallelComput., 33 (2007) 541.[2] Neri A., Esposti Ongaro T., Macedonio G. and Gidaspow D., J. Geophys. Res., 108(2003) 2202.[3] de’ Michieli Vitturi M., Esposti Ongaro T., Neri A., Salvetti M. V. and Beux F.,Comput. Geosci., 11 (2007) 183.[4] Neri A., Esposti Ongaro T., Menconi G., de’ Michieli Vitturi M., Cavazzoni C.,Erbacci G. and Baxter P. J., Geophys. Res. Lett., 34 (2007) L04309.[5] Esposti Ongaro T., Neri A., Menconi G., de’ Michieli Vitturi M., Marianelli P.,Cavazzoni C., Erbacci G. and Baxter P. J., J. Volcanol. Geoth. Res., 178 (2008) 378.[6] Esposti Ongaro T., Clarke A. B., Neri A., Voight B. and Widiwijayanti C., J.Geophys. Res., 113 (2008) B03211.

http://eprints.bice.rm.cnr.it/16474/1/ncc9370.pdf

An application of parallel computing to the simulation of volcanic eruptions

Abstract

Similar works

Full text

Available Versions

Earth-prints

Scientific Open-access Literature Archive and Repository