GPUSPH: a Smoothed Particle Hydrodynamics model for the thermal and rheological evolution of lava flows

Abstract GPUSPH is a fully three-dimensional model for the simulation of the thermal and rheological evolution of lava flows that relies on the Smoothed Particle Hydrodynamics (SPH) numerical method. Thanks to the Lagrangian, meshless nature of SPH, the model incorporates a more complete physical description of the emplacement process and rheology of lava that considers the free surface, the irregular boundaries represented by the topography, the solidification fronts and the non-Newtonian rheology with temperature-dependent parameters. GPUSPH follows the very general Herschel–Bulkley rheological model, which encompasses Newtonian, power-law and Bingham flow behaviours, with both constant and temperature-dependent parameters, and can thus be used to explore in detail the impact of rheology on the behaviour of lava flows and on their emplacement. To illustrate this possibility, we present some preliminary applications of the model for studying the rheology of lava flows with different constitutive relationships and thermal regimes using the real topography of the Mt Etna volcano.

[1]  Robert A. Dalrymple,et al.  SPH on GPU with CUDA , 2010 .

[2]  Dominique Laurence,et al.  Unified semi‐analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method , 2013 .

[3]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[4]  Benedict D. Rogers,et al.  Numerical Modeling of Water Waves with the SPH Method , 2006 .

[5]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[6]  G. M. Crisci,et al.  Lava Flow Simulation Bv A Discrete Cellular Model: First Implementation , 1986 .

[7]  C. Negro,et al.  An emergent strategy for volcano hazard assessment: From thermal satellite monitoring to lava flow modeling , 2012 .

[8]  Giovanni Gallo,et al.  Porting and optimizing MAGFLOW on CUDA , 2011 .

[9]  M. Gómez-Gesteira,et al.  Boundary conditions generated by dynamic particles in SPH methods , 2007 .

[10]  D. Dingwell,et al.  The onset of non-Newtonian rheology of silicate melts , 1990 .

[11]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[12]  Barbara Scherllin-Pirscher,et al.  A new dynamic approach for statistical optimization of GNSS radio occultation bending angles for optimal climate monitoring utility , 2013 .

[13]  M. Favalli,et al.  Forecasting lava flow paths by a stochastic approach , 2005 .

[14]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[15]  J. E. Guest,et al.  Mount Etna: The anatomy of a volcano , 1985 .

[16]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[17]  L. Fortuna,et al.  Simulations of the 2004 lava flow at Etna volcano using the magflow cellular automata model , 2008 .

[18]  Ciro Del Negro,et al.  Forecasting lava flow hazards during the 2006 Etna eruption: Using the MAGFLOW cellular automata model , 2009, Comput. Geosci..

[19]  M. Rajeevan,et al.  Nowcasting severe convective activity over southeast India using ground‐based microwave radiometer observations , 2013 .

[20]  K. Ishihara,et al.  Numerical Simulation of Lava Flows on Some Volcanoes in Japan , 1990 .

[21]  F. Garel,et al.  An analogue study of the influence of solidification on the advance and surface thermal signature of lava flows , 2014 .

[22]  M. Dragoni,et al.  Downslope flow models of a Bingham liquid: Implications for lava flows , 1986 .

[23]  P. Cleary,et al.  Conduction Modelling Using Smoothed Particle Hydrodynamics , 1999 .

[24]  Sho Sasaki,et al.  Simulating lava flows by an improved cellular automata method , 1997 .

[25]  R. C. Kerr,et al.  Importance of surface crust strength during the flow of the 1988–1990 andesite lava of Lonquimay Volcano, Chile , 2007 .

[26]  Giovanni Macedonio,et al.  Computational modeling of lava flows: A review , 2005 .

[27]  A. Harris,et al.  FLOWGO: a kinematic thermo-rheological model for lava flowing in a channel , 2001 .

[28]  Michael Manga,et al.  Kinematics and dynamics of lava flows , 2005 .

[29]  Mahesh Prakash,et al.  Discrete–element modelling and smoothed particle hydrodynamics: potential in the environmental sciences , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[30]  M. Mcpherson,et al.  Introduction to fluid mechanics , 1997 .

[31]  M. Dragoni,et al.  The effect of crystallization on the rheology and dynamics of lava flows , 1994 .

[32]  Harry Pinkerton,et al.  Lava tube morphology on Etna and evidence for lava flow emplacement mechanisms , 1999 .

[33]  Paul W. Cleary,et al.  Three-dimensional smoothed particle hydrodynamics simulation of high pressure die casting of light metal components , 2002 .

[34]  Daniel De Kee,et al.  Non-Newtonian fluids with a yield stress , 2005 .

[35]  Giovanni Gallo,et al.  Scalable multi-GPU implementation of the MAGFLOW simulator , 2011 .

[36]  Dinesh Kumar,et al.  Parallel Godunov smoothed particle hydrodynamics (SPH) with improved treatment of Boundary Conditions and an application to granular flows , 2013, Comput. Phys. Commun..

[37]  Db Dingwell,et al.  Viscosity of hydrous Etna basalt: implications for Plinian-style basaltic eruptions , 2002, Bulletin of Volcanology.

[38]  P. Cleary,et al.  Three dimensional modelling of lava flow using Smoothed Particle Hydrodynamics , 2011 .

[39]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[40]  R. W. Griffiths.  The Dynamics of Lava Flows , 2000 .

[41]  C. Negro,et al.  Lava flow hazards at Mount Etna: constraints imposed by eruptive history and numerical simulations , 2013, Scientific Reports.

[42]  Eugenio Rustico,et al.  Numerical simulation of lava flow using a GPU SPH model , 2011 .

[43]  J. Monaghan,et al.  Solidification using smoothed particle hydrodynamics , 2005 .

[44]  D. L. Peck,et al.  The viscosity of basaltic magma; an analysis of field measurements in Makaopuhi lava lake, Hawaii , 1968 .

[45]  T. Papanastasiou.  Flows of Materials with Yield , 1987 .

[46]  Robert Wright,et al.  Using infrared satellite data to drive a thermo‐rheological/stochastic lava flow emplacement model: A method for near‐real‐time volcanic hazard assessment , 2008 .

[47]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[48]  C. Connor,et al.  Probabilistic approach to modeling lava flow inundation: a lava flow hazard assessment for a nuclear facility in Armenia , 2012, Journal of Applied Volcanology.

[49]  A. Vicari,et al.  Near‐real‐time forecasting of lava flow hazards during the 12–13 January 2011 Etna eruption , 2011 .

[50]  Ioan Nistor,et al.  A corrected 3-D SPH method for breaking tsunami wave modelling , 2011, Natural Hazards.

[51]  M. Dragoni,et al.  Role of heat advection in a channeled lava flow with power law, temperature‐dependent rheology , 2013 .

[52]  Richard V. Craster,et al.  Dynamics of cooling domes of viscoplastic fluid , 2000, Journal of Fluid Mechanics.

[53]  Manuel Pastor,et al.  A SPH Depth Integrated Model for Popocatepetl 2001 Lahar. , 2009 .

[54]  Alicia García,et al.  Assessment and Modelling of Lava Flow Hazard on Lanzarote (Canary Islands) , 2001 .

[55]  Harry Pinkerton,et al.  Methods of determining the rheological properties of magmas at sub-liquidus temperatures. , 1992 .

[56]  Ciro Del Negro,et al.  Modeling of the 2001 lava flow at Etna volcano by a Cellular Automata approach , 2007, Environ. Model. Softw..

[57]  Tjondro Indrasutanto,et al.  Dynamics of Lava Flows , 2009 .

[58]  Harry Pinkerton,et al.  Rheological properties of basaltic lavas at sub-liquidus temperatures: laboratory and field-measurements on lavas from Mount Etna. , 1995 .

[59]  D. Dingwell,et al.  Non-Newtonian Rheology of Igneous Melts at High Stresses and Strain Rates: Experimental Results for Rhyolite, Andesite, Basalt, and Nephelinite , 1990 .

[60]  Giovanni Russo,et al.  Sensitivity analysis of the MAGFLOW Cellular Automaton model for lava flow simulation , 2012, Environ. Model. Softw..

[61]  L. Fortuna,et al.  Lava flow simulations using discharge rates from thermal infrared satellite imagery during the 2006 Etna eruption , 2009 .