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 (

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.

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. Simulation of all possible hazards with one model is difficult due to the fact that different length scales dominate different hazards. Our focus here is the hazard that volcanic ash poses to aircraft.

During volcanic eruptions, 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

Several one-dimensional (1-D) volcanic plume models have been developed in
the past few decades, ranging from the most basic 1-D model

The development of 2-D and 3-D time-dependent and multiphase numerical
models for volcanic plumes has provided new explanations for many features of
explosive volcanism. For example, a recent study based on a 3-D fluid dynamical
model

Another 3-D model, SK-3D

While SK-3D focuses on accurately capturing the entrainment caused by
turbulent mixture with higher resolution and numerical method of higher
order, PDAC takes the disequilibrium between different phases into account
and hence is a true multiphase model. Another 3-D model, the Active Tracer
High-Resolution Atmospheric Model (ATHAM)

Besides adding to their special strengths (ATHAM has been adding more and more microphysics; PDAC was extended to consider more phases), these models are also adding core strengths. PDAC development has begun to include the effect of microphysics into the model, while ATHAM development has extended its ability to modeling pyroclastic flow. Both are using finer and finer resolution.

Recently, a first-order, non-equilibrium compressible 3-D model, ASHEE

To summarize, each 3-D model has its own focus based on the problem of interest and modeling/numerical choices made. Accuracy of simulation (depending on comprehensiveness of the model, resolution of discretization, numerical error and order of accuracy) and the simulation time (depending on number of governing equations, resolution, numerical methods and parallel techniques) are always conflicting considerations in 3-D plume simulations.

To the best of our knowledge, all of the existing 3-D plume models use
mesh-based Eulerian methods, and there are no 3-D plume models based on mesh-free
Lagrangian methods. Lagrangian methods have several features that are
suitable for volcanic plume simulation that we outline below. Among such
Lagrangian methods, smoothed particle-hydrodynamics-based simulations

better investigation of mixing phenomena;

accurate modeling of the development of the zone of flow establishment (ZFE), zone of established flow (ZEF) investigation and relation to column collapse and the questions relating to the development of entrainment; and

easy inclusion of particles of different sizes (phases) and investigation of detailed mechanics of sedimentation and drag force interaction in lower plume.

These are enabled by the following features of SPH:

The advection term in the Navier–Stokes equations does not appear explicitly in
discretized formula of SPH (as illustrated in
Eqs.

It is easy to include various physics effects (like self gravity, radiative
cooling and chemical reaction) in the model. It does not require a major overhaul
and re-tooling every time new physics is introduced

With more than one phase, each described by its own set of particles, interface problems between phases are often trivial for SPH but difficult for mesh-based schemes. Thus, multiphase flow can be easily handled by SPH. Adding new phases to the model also does not require a major overhaul and re-tooling. As will be shown in later paragraphs, adding new phases only leads to adding several lines into the source code for new phases and additional interaction terms between existing phases and newly added phases.

Interface tracking is explicit in SPH through capturing of the locations of the particles. Less numerical effort is required for interface construction when we attempt to include the effects of mixing by resolving the detailed interface structure and dynamics of turbulence.

As discussed in the previous paragraph, existing 3-D plume models focus on one or several specific aspects of the plume and have been extended to be more comprehensive by accounting for more physics or more phases. Easy extensibility and capability of handling multiple phase flow with less additional numerical effort greatly facilitate future extension of SPH models. As volcanic plumes are in nature multiphase and without predefined boundary in the atmosphere, SPH is a suitable numerical method for plume modeling. The core physics, such as entrainment of air and thermal expansion, are essential for all plume modeling, while some other physics, such as water condensation and aggregation, are important in specific scenarios. As an initial effort towards exploiting advantages of SPH in volcanic plume modeling, we focus on capturing basic features in plume development using a numerically robust and computationally efficient framework with support for scalable parallel computing.

Open-source availability and the relatively easy extensibility of SPH will facilitate development of a more comprehensive community-driven model.

Even though SPH has been known for several decades, implementations of SPH
for compressible multiphase turbulent flows are few.

Several issues endemic to classical SPH, like tensile instabilities, compressible turbulence modeling and turbulent heat exchange, are fixed in our implementation. The most popular applications of SPH (and their original motivating application) have been in the simulation of free surface flow, such as breaking waves and floods. Less attention was paid to velocity inlet and pressure outlet boundary conditions which are required in plume modeling.

We develop methodology to impose pressure boundary conditions by adding extra layers of static ghost particles. Additional constraints on the time step are used to avoid the growth of numerical fluctuations near the pressure boundary. We impose a velocity inlet boundary condition by placing several layers of ghost particles moving with eruption velocity.

The turbulence model is crucial for reproducing the entrainment of air. There
are several turbulence models proposed for the SPH method

Corrected formulation of SPH

Simulation of volcanic plumes with acceptable accuracy requires fine resolution (very high particle counts) that cannot be accomplished without parallel computing using large process counts. The core solver of our model is parallelized by distributed memory message passing interface (MPI) standard parallelism. In addition, a dynamic load balancing strategy is also developed.

Imposition of some types of boundary conditions (such as eruption boundary condition) requires dynamically adding and removing of particles during simulation. To address this issue, we adopt an efficient data management scheme based on a time-dependent space-filling curve (SFC) induced indexing and hash table. The computational cost is further reduced by adjusting the simulation domain adaptively.

The physical model of the plume is first presented in
Sect.

During an explosive eruption, a volcanic jet erupts out from a vent with a
speed of several tens to more than 150 m s

All in all, the process of plume development is essentially a multiphase turbulent mixing process coupled with heat transfer and other microphysical and chemical reactions.

As an initial effort towards exploiting the feasibility and advantage of SPH in
plume modeling, our model is designed to describe an injection of well-mixed
solid and volcanic gas from a circular vent above a flat surface into a
stratified stationary atmosphere following SK-3D

Because of the above assumptions, all other microphysical processes (such as
the phase changes of

Based on above assumptions, the governing equations of our model are given as
(which is the same as the governing equations of SK-3D)

In mesh-based methods, governing equations in Eulerian form,
Eqs. (

In the current model, the initial domain is a box. The boundaries are categorized as the velocity inlet (a circular area at the center of the bottom of the box), wall boundary (box bottom) and pressure outlet (other faces of the box).

At the vent, the temperature of erupted material

Velocity is zero for the non-slip wall boundary. If we assume the boundary to be
adiabatic, heat flux should be zero on the boundary. The flux of mass should
also be zero. As a result, internal energy flux, which consists of heat flux
and energy flux carried by mass flux, vanishes on the wall boundary.
Equations (

The pressure of the surrounding atmosphere is given. Except for the pressure,
boundary values for density, velocity and energy on the outlet should depend
on the solution. As we ignore the viscosity, the shear stress is ignored and
normal stress (whose magnitude equals its pressure) balances the ambient
pressure.

SPH is a mesh-free Lagrangian method. In SPH, the domain is discretized by a
set of particles or discretization points and the position of each particle
is updated at every time step based on the motion computed. Approximation of
all field variables (velocity, density and pressure, etc.) is obtained by
interpolation based on discretization points. The physical laws (such as
conservation laws of mass, momentum and energy) written in the form of partial differential equations
(PDEs) or ordinary differential equations (ODEs)
need to be transformed into the Lagrangian particle formalism of SPH. Using a
kernel function that provides the weighted estimation of the field variables
at any point, the integral equations are estimated as sums over particles in
a compact subdomain defined by the support of the kernel function associated
with the discretization points. Thus, field variables associated to the
particle are updated based on its neighbors. Each kernel function has a
compact support determined by the smoothing length of each particle. There are
several review papers by

There are several procedures for discretizing governing equations (PDEs or
ODEs) with SPH. We present here one of them following

The weighting function also needs to satisfy conditions such as positivity and compact support. In addition, the kernel function must be monotonically decreasing with the distance between particles.

There is a wide variety of possible weighting functions that can satisfy
these requirements, such as spline functions (with different orders) and
Gaussian functions. Generally, the accuracy increases with the order of the
polynomials of the kernel function, but the computational cost also increases
as the number of interactions increases. We adopt a truncated Gaussian
function as the weighting function in our simulation.

By replacing the

In classical SPH, shock waves are handled by introducing artificial viscosity, a term that is defined based on second derivatives of velocity, to smear out discontinuities. As in the case of first-order derivatives, second-order derivatives can be estimated by differentiating a SPH interpolation twice. However, such a formulation has two disadvantages: first, it is very sensitive to irregular distribution of particles; second, the second derivative of the kernel can change sign and lead to unphysical representations (for example, viscous dissipation causes decrease of the entropy).

One of the most commonly used models of artificial viscosity

The SPH viscosity can be related to a continuum viscosity by converting the
summation to integrals

The basic interpolation given in
Eqs. (

We highlight an important feature of the SPH methodology. Adding new physics
and new phases into the model is trivial in terms of discretization. For
example, adding a new source (or sink) into Eq. (

The physical quantities (velocity, density and pressure) and particle
position change every time step. The Courant condition, which is in spirit
similar to the Courant condition for the mesh-based methods, is used to
determine the time step

First-order Euler integration, with

The classical SPH method was known to suffer from tensile instability and
boundary deficiency. Tests of the standard SPH method indicate an instability
in the tensile regime, while the calculations are stable in compression. A
simple example of such a test calculation exhibiting the instability involves
a body which is subject to a uniform initial stress, either compressive or
tensile. If the initial stress is tensile, a very small velocity perturbation
on a single particle can lead to particles clumping together, forming large
voids and seriously corrupting density distribution. But if the initial
stress is compressive, the small velocity perturbation on a single particle
cannot lead to any changes in particle distribution

For problems of higher dimension, the expressions for function approximation
are exactly the same as Eq. (

Air and erupted material are represented by two different sets of SPH
particles (or discretization points) in the model. Based on assumptions we
made in Sect.

In areas far away from the interface, updating of density is exactly the same
as that for single-phase flow. For example, on the right side and left side
(or blue areas) in Fig.

In panel

Interface construction will become necessary and important when attempting to
include the effects of mixing by resolving the detailed interface structure
and dynamics of turbulence. As a Lagrangian method, interface tracking in SPH
is explicit through capturing of the locations of the particles, much
simpler than Eulerian methods. The existence of complex evolving interfaces
between phases presents severe challenges to conventional Eulerian grid-based
numerical methods. Either interface tracking (Lagrangian)

For high-speed shearing flow, the momentum exchange and heat transfer are
dominated by turbulent fluctuations as turbulent exchange coefficients are
several magnitudes larger than corresponding physical coefficients (molecular
viscosity and heat conduction coefficient). In addition to momentum and energy
exchange, mixing between plume and air is important in plume modeling.
Quantifying these mixing processes in real implementation is challenging
because of the scale disparity between the large-scale fluid motion and the
diffusion processes on interface that ultimately lead to mixing. Ideally, one
would like to be able to include the effects of mixing on the large-scale
dynamics without resolving the detailed interface structure and dynamics of
turbulence to reduce computational cost. To resolve all turbulent exchange at
all different scales and sub-particle-scale mixing with relative coarse
resolution, a SPH sub-particle-scale (SPH-SPS) turbulence models should be included. Among existing
SPH-SPS turbulence models

The average of physical quantities over space introduces extra terms into the
governing equations. Once the form of the smoothing (average) is chosen, these
extra terms are determined. The typical LANS model uses a smoothed velocity

It is a common practice in LANS to use a differential equation for the
smoothing rather than the integral form and finally reach a system of
equations that need to be solved implicitly. In the

The smoothing adopted by

For compressible flow, the energy equation is coupled with the momentum
equation and mass conservation equation. Averaging of thermal energy over
space introduces some additional terms besides the stress term induced by
velocity average

We adopt the Reynolds analogy to get the heat transfer coefficient due to
turbulence. The Prandtl number is defined as

However, the above equation is correct only for the 1-D situations. For 2-D
or 3-D, it is not easy to get an explicit expression. We adopt an alternative
way: obtaining a value for each pair of particles instead of persisting on
getting an analytical expression. Choosing the smoothing function to be the same
as the SPH kernel and the smoothing length scale

A cross-section view of the simulation domain in the

The heat conduction equation without the source term is

Plugging in the discretized turbulent stress term and turbulent heat transfer
term into the momentum and energy equation, we get new discretized governing
equations:

All boundary conditions are imposed by ghost particles.
Figure

Traditionally, either ghost particles that mirror real particles across the
boundary

A natural way of imposing eruption boundary condition is using ghost
particles that move with the eruption velocity and bear the temperature of
the erupted material. A parabolic velocity profile that represents a fully
developed Hagen–Poiseuille flow is used to determine the inlet particle
velocity. The detailed shape of the parabolic profile is determined based on
an averaged eruption velocity (Eq.

Another boundary condition in our model is the pressure outlet boundary. For
flow in a straight channel, it is possible to treat the exit the same as the
entry with a prescribed velocity profile. For flow with a more complex channel,
an exit far downstream of the flow disturbance is also feasible. However, the
natural boundary condition (Eq.

As simulations progress, changes in position and physical quantities of real
particles near pressure boundaries might corrupt the pressure boundary condition
that was established initially. This shortcoming is relieved by choosing a
larger computational domain so that boundaries that might be corrupted are
far away from turbulent mixing area. In addition, to avoid enlarging
fluctuations, we add another constraint on the time step:

One disadvantage of the 3-D model is that it usually takes a much longer time
than 1-D models to complete one simulation. This disadvantage further
prevents simulation with finer resolution and accounting for more
physics in one model. Non-intrusive uncertainty analysis, which is commonly
adopted in hazard forecasting, requires finishing multiple simulations within
a given time window. High-performance computing is therefore essential. Among
existing CPU parallel SPH schemes, most of them focus on the neighbor search
algorithm and dynamic load balancing

The time complexity for an SPH method is

In DualSPHysics

The parallelization is achieved by splitting computational domain into
subdomains. Each subdomain is computed by a single processor. For any
subdomain, information from its neighboring subdomains is required when
updating physical quantities. To guarantee consistency, data are synchronized
if physical quantities are updated. Even though more complicated graph-based
partitioning tools

More details about the data structure, domain decomposition, load balancing,
domain adjusting and performance benchmarking have been published separately

Strong scalability test result.

Weak scalability test result.

The effect of domain adjusting on simulation time.
Panel

Performance tests have been carried out on the computational cluster of Center for Computational Research
(CCR) at the University at Buffalo. Intel Xeon
E5645 CPUs running at 2.40 GHz clock rate with 4 GB memory per core on a
Q-Logic Infiniband are used in these tests. Each node is comprised of two
sockets with six of these cores. Memory and level 3 cache are shared on each
node. The initial domain is [

The weak scalability test is conducted with the same initial domain and
various smoothing lengths. Each simulation runs for 400 time steps. The
average number of real particles of each process keeps constant at 25 900.
As shown in Fig.

We present a series of numerical simulations to verify and validate our model in this section. Plume-SPH is first verified by 1-D shock tube tests, then by a JPUE (jet or plume that is ejected from a nozzle into a uniform environment) simulation. Velocity and mass fraction distribution both along the central axis and cross transverse are compared with experimental results. The pattern of ambient particle entrainment is also clearly shown. Then, a simulation of representative strong volcanic plume is conducted. Integrated local variable are comparable with simulation results from existing 3-D plume models.

1-D shock tube tests are first conducted to verify our code. Input parameter
of each tests can be found in Table

Input parameters of 1-D shock tube tests.

In Table

Comparison of specific internal energy of simulation results against analytical results for shock tube tests. The plots from left to right correspond to test 1, test 2 and test 3, respectively.

JPUE can be considered as a simplified volcanic plume. While the effect of
stratified atmosphere and the effect of expansion due to high temperature in
volcanic plume are not represented, JPUE reproduces the entrainment due to
turbulent mixing which is one of the key elements in the volcanic plume
development. There exist consistently good experimental data

As many of these experiments were conducted with liquid, we replace the
original equation of state (Eq.

One overall feature of JPUE is “self-similarity”, which means that the evolution of the JPUE is determined solely by the local scale of length and velocity, which theoretically account for the fact that the rate of entrainment at the edge of JPUE is proportional to a characteristic velocity at each height. As a result, physical and numerical experiments do not necessarily have exactly the same setups and are compared on a non-dimensional basis.

List of eruption condition for the test cases.

Dimensionless concentration and velocity distribution across the cross section.

Panel

A three-dimensional axisymmetric JPUE which ejects from a round vent is
simulated with eruption parameters listed in
Table

Although both velocity and concentration are found to be well matched with
experimental results, a small disparity in both velocity and concentration
is observed near the boundary of the jet, which is possibly caused by
overestimation of the drag effect by standard SPH

We also investigated the mixing due to turbulence in the JPUE simulation by
checking the mixture of the two phases. It is shown in
Fig.

Panel

The development of a volcanic plume is more complicated than JPUE in several aspects. Besides turbulent entrainment of ambient fluids, development of the volcanic plume also involves heating of entrained air and expansion in a stratified atmosphere. A strong eruption column without wind is tested in this section for the purpose of further verification and validation. Both global variables and local variables are compared with existing models.

Eruption parameters, material properties and atmosphere are chosen to be the
same as the strong plume no-wind case in a comparison study on eruptive
column models by

List of material properties.

Mass fraction for

Figure

One of the key global quantities of great interest is the altitude to which
the plume rises. The top height predicted by our model is around 40 km which
agrees with other plume models. For example, the height predicted by PDAC is
42 500 m, by SK-3D is 39 920 m, by ATHAM is 33 392 m and by ASHEE is
36 700 m. As for local variables, the profiles of integrated temperature,
density, mass fraction of entrained air, gas mass fraction, mass fraction of
solid materials and the radius of the plume as a function of height are compared with
existing 3-D models in
Figs.

Temperature as a function of height.

The mass fraction of entrained air, gas and solids as a function of height.

As particles distribute irregularly in the space in SPH simulation results, we need to project simulation results (on irregular particles) onto a predefined grid before doing time-average and spatial integration. See Appendix A for more details of postprocessing.

The profiles of local variables match well with simulation results of existing 3-D models in a general sense. The basic phenomena in volcanic plume development are correctly captured by our model.

Density of the strong plume without wind after reaching its top height.

As the height increases, the amount of entrained air also increases. Around
the neutral height, where the umbrella expands, the entrainment of air shows
a slight decrease due to lack of air surrounding the column at that height.
The profile for gas, which accounts for both air and vapor, shows a very
similar tendency to that of entrained air. Recall that vapor condensation is
not considered in our model. In addition, we assume that erupted material
behaves like a single-phase fluid. So the mass fraction of gas is simply a
function of entrained air (Eq.

Among these 3-D models, ATHAM takes vapor condensation into account and
Eq. (

Radius of the strong plume without wind after reaching its top height.

PDAC, which treats particles of two different sizes as two separate phases, predicted a similar mass fraction profile. That implies that assumption of dynamic equilibrium in our model is at least valid for eruptions similar to the test case.

With more cool air entrained into the plume and mixing with the hot erupted
material, the temperature of the plume decreases as the height increases as
shown in Fig.

Our model adopts the same assumptions and governing equations as SK-3D. However, there is still an obvious disparity between the profiles of local variables of our model and SK-3D. One of the big differences between these two models is that we adopt a LANS type of turbulence model while SK-3D adopts a large eddy simulation (LES) turbulence model. This implies that choice of turbulence model might play a critical role in plume simulation.

A new plume model was developed based on the SPH method. Extensions necessary for Lagrangian methodology and compressible flow were made in the formulation of the equations of motion and turbulence models. Advanced numerical techniques in SPH were exploited and tailored for this model. High-performance computing was used to mitigate the tradeoff between accuracy (which depends on comprehensiveness of the model, resolution, order of accuracy of numerical methods, scheme for time upgrading) and simulation time (which depends on comprehensiveness of model, resolution, order of accuracy of numerical methods, scheme for time upgrading, etc. and computational techniques). The correctness of the code and model was verified and validated by a series of test simulations. Typical 1-D shock tube problems were simulated and compared against analytical results showing good agreement. Dimensionless velocity and concentration distribution across the cross section and along the jet axis match well with experimental results of JPUE. Top height and integrated local variables simulated by our model are consistent with simulation results of existing 3-D plume models. Comparison of our results with those of SK-3D implies that the turbulence model plays a significant role in plume modeling.

Currently existing 3-D models focus on certain aspects of the volcanic plume
(PDAC on pyroclastic flow, ATHAM on microphysics and SK-3D on entrainment
with higher resolution and higher order of accuracy), and hence, naturally,
different assumptions were made in these models. However, these different
aspects of volcanic plumes are not independent but are actually coupled. For
example, it has been illustrated by

We have presented in this paper an initial effort and results towards
developing a first principle-based plume model with comprehensive physics,
adopting proper numerical tools and high performance computing. More advanced
numerical techniques, such as adaptive particle size, Godunov-SPH,
semi-explicit time-advancing schemes and better data management strategies and
algorithms are on our list to exploit in the future. In the near future,
the effect of wind field will be taken into account. Our code will also be made
available in the open-source form for the community to enhance. Besides
improving the plume model, coupling the volcanic plume model with magma reservoir
models

The Plume-SPH code, together with a user manual providing
instructions for installation, running and visualization, is archived at

The input data for all simulations presented in this work are archived in the
same repository. The MIT license governs the distribution and use of the code
and associated documentation files. Permission is granted, free of charge, to
any person to deal with the software without restriction. The complete
copyright statement can be found in the repository:

User manual and input data for test runs are also archived in the same repository.

Output data of simulations presented in the paper are around tens of gigabytes and are archived in UBbox. Access will be provided to all upon request.

Procedure of projection of simulation results carried by particles
onto regular grids, as shown in these figures from left to right:

Particles distribute irregularly in SPH simulation results. To adapt
postprocessing originally proposed for the mesh-based method, we need to project
simulation results onto a predefined regular mesh. As shown in
Fig.

obtain raw simulation results carried by particles that irregularly distribute in the space,

create regular grids,

search for neighbor particles for each node of the regular grids and

interpolate physical quantities from neighbor particles onto the corresponding node of
regular grids according to Eq. (

ZC was the primary developer of the Plume-SPH code. All co-authors contributed equally to the formulation, analysis and writing of this paper.

The authors declare that they have no conflict of interest.

All developers of Titan-2D, especially Dinesh Kumar who developed the GSPH version of Titan-2D, are greatly appreciated as Plume-SPH is based on their code. Advice and data (which are not shown in this paper) given by Suzuki Yujiro gave us great help at the initial stage of model establishment and therefore are greatly appreciated. We appreciate Tomaso Esposti Ongaro for providing simulation data of PDAC (also provided by Antonio Costa later, together with simulation results of other plume models) which helped us in early verification and improvement. We appreciate Antonio Costa for providing simulation results of existing 3-D models, which are used in the verification and validation section of this paper. We thank Matteo Cerminara for his help on postprocessing of plume simulation results and his careful review of our manuscript and constructive remarks. Comments by another anonymous reviewer are appreciated as well. Computational results reported here were performed at the Center for Computational Research at the University at Buffalo. This project is supported by grant no. NSF ACI/1131074 from the National Science Foundation. Edited by: Adrian Sandu Reviewed by: Mattia de' Michieli Vitturi and one anonymous referee