Plume-SPH 1.0: a three-dimensional, dusty-gas volcanic plume model based on smoothed particle hydrodynamics
Authors: Cao Zhixuan , Patra Abani , Bursik Marcus , Pitman E. Bruce , Jones Matthew 
Published: July 2018

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.