In what follows I make a quick inventory of the main codes of computational geodynamics,
for crust, lithosphere and/or mantle modelling. In order to find all CIG-codes citations go to:
https://geodynamics.org/cig/news/publications-refbase/
Belonging to the same family as the FLAC (Fast Lagrangian Analysis of Continua; Cundall and Board,
1988 [477]) and Parovoz codes (Poliakov and Podladchikov, 1992 [1683]; Gerbault et al. , 2009
[718]), ADELI is based on an explicit temporal finite difference approach associated with the
dynamic relaxation method (Underwood, 1983). Numerical and mechanical aspects of this code
in a 2-D or 3-D context can be found in Hassani et al. (1997) [871] and Chéry et al. (2001)
[371].
The program permits a spatially variable Newtonian or non-Newtonian viscosity in a 2-D geometry with
boundary conditions on traction and/or velocity. It is also possible to include a single fault or discontinuity
in the problem in a dynamically self consistent way. The 2-D deformation field represents either plane-strain
deformation, or it permits a specified distribution of normal stress in the third direction. The latter is
referred to as the thin viscous sheet formulation when the normal force is due to gravity acting on variations
of the layer thickness. Plane-stress calculations are a specific case of the thin viscous sheet
formulation.
The programs basil and sybil have been developed mainly at Monash University since 1988, and before
that at ANU and Harvard. The present set of programs has been developed mainly by Greg Houseman,
Terence Barr and Lynn Evans.
ELLE is an open-source multi-process and multi-scale software for the simulation of geologic processes,
especially (but not only) during deformation and metamorphism. It is coupled to/based on BASIL. See
http://elle.ws/ for a complete list of publications.
Citcom (California Institute of Technology COnvection in the Mantle) was developed by Louis Moresi at
the California Institute of Technology (Moresi, 1992). This code solved the equations of viscous fluid
dynamics, and, as the name implies, was geared towards modelling convection in the Earth’s mantle. Moresi
and Solomatov (1995) provide a detailed description of the multigrid finite element algorithm. After this
and during his time at CSIRO, Dr. Moresi modified the code to include mobile integration points. The code
became a particle-in-cell finite-element code named CItcom , which was able to track and evolve material
properties on particles. This work at CSIRO resulted in a new generation of the software, named
Ellipsis.
It is a massively parallelized finite element software package for modeling elastic and viscoelastic
deformation on regional and global scales due to surface loads or tidal loads. It employs a Lagrangian
deformable grid and works for 3-D Cartesian, regional spherical, and global spherical geometries, and was
first developed from CitcomS It incorporates dynamic sea-level equation, degree-1 motion, true polar
wander, and mantle compressibility. The package makes use of massively parallel computations that enables
high resolution and efficient modeling. As these loading models share similar numerical algorithms
and finite element structures to their counterparts of convection models, they are benefitted
directly from new developments to convection models including non-linear rheology and parallel
computing.
SCAM (Spherical Convection in an Axisymmetric Mantle) is a spherical, axisymmetric version of the
finite element code ConMan (!). It is used in Kellogg & King (1997) [1088], King (1997) [1117], Kiefer &
Kellogg (1998) [1103], Kiefer (2003)[1102], Redmond & King (2004) [1739], Li & Kiefer [1243], Kiefer & Li
[1104]. Also probably [616] and [620].
By critically evaluating the strengths and weaknesses of the FLAC algorithm, Choi et al. (2013) created a
new code, DynEarthSol2D, and Tan et al. (2013) [AGU abstract] further extended it to three dimensions,
DynEarthSol3D. DynEarthSol3D (Dynamic Earth Solver in three Dimensions) is a robust, flexible, open
source finite element code for modeling non-linear responses of continuous media and thus suitable for
long-term tectonic modeling. https://github.com/tan2/DynEarthSol
Elmer is an open source multiphysical simulation software mainly developed by CSC - IT Center for
Science (CSC). Elmer development was started 1995 in collaboration with Finnish Universities,
research institutes and industry. Elmer includes physical models of fluid dynamics, structural
mechanics, electromagnetics, heat transfer and acoustics, for example. These are described
by partial differential equations which Elmer solves by the Finite Element Method (FEM).
https://www.csc.fi/web/elmer
The FEniCS Project is a modern collection of open source software components directed at the automated
solution of differential equations by finite element methods.
GeoFEST (Geophysical Finite Element Simulation Tool) is a two- and three-dimensional finite element
software package for the modeling of solid stress and strain in geophysical and other continuum domain
applications. The physics models supported include isotropic linear elasticity and both Newtonian and
power-law viscoelasticity, via implicit quasi-static time stepping. In addition to triangular, quadrilateral,
tetrahedral and hexahedral continuum elements, GeoFEST supports split-node faulting, body forces, and
surface tractions.
Rather logically only a handful of publications were produced with this code:
(LAgrangian Particle EXplicit, based on the prototype code PAROVOZ)
LARGE 0.2.0 (Lithosphere AsthenospheRe Geodynamic Evolution) is a geodynamic modelling Python
package that implements a flexible and user friendly tool for the geodynamic/modelling community. It
simulates 2D large scale geodynamic processes by solving the conservation equations of mass, momentum,
and energy by a finite difference method with the moving tracers technique. LARGE uses advanced modern
numerical libraries and algorithms but unlike common simulation code written in Fortran or C this code is
written entirely in Python.
[Taken from tojn23] The initial CAGES algorithm developed by Fernŕndez et al. (1990) was improved by
incorporating the geoid anomaly, which allowed for better control of the density dis- tribution at the
lithospheric mantle scale. The algorithm was used to study the litho- sphere in different geodynamic
scenarios, as is the case of the Atlantic margin (Torne et al. 1995), the Cantabrian margin (Ayarza et al.
2004), the transition from the Iberian Massif to the oceanic crust of the Gulf of Cádiz (Fernŕndez et al.
2004), the NW margin of Morocco and the Atlas mountains (Zeyen et al. 2005; Jiménez-Munt et al. 2010),
the Western Mediterranean (Roca et al.2004), or the Variscan terrain of the SW of the Ibe- rian
Peninsula (Palomeras et al. 2011), among other studies. Subsequently, geochemical and petrological
data of the mantle were incorporated (Afonso et al. 2008) and the pos- sibility of introducing
thermal, seismic, or compositional anomalies, or a combination of them into the sublithospheric
mantle (Kumar et al. 2020), has improved the potential of these algorithms (LitMod2D code)
considerably. For examples applied to the study of the Iberian Peninsula, we refer to the works of
Carballo et al. (2015a, b), Pedreira et al. (2015), Jiménez-Munt et al. (2019), and Kumar et al.
(2021).
The code models the equations of infinite Prandlt number, incompressible viscous flow, and
thermal transport. It employs s fixed two-dimensional Eulerian grid of triangular elements each
containing six nodal points. This allows for quadratic interpolation of velocities and temperatures.
Galerkin’s method is used to produce the numerical equations [Sato and Thompson, 1976;
Schubert and Anderson, 1985]. Because of the need for a large number of nodal points to resolve
the temperature and velocity fields (approximately 6600 nodes and and 3200 elements were
employed in each calculation), the penalty method, with a penalty parameter (bulk viscosity
of an element divided by shear viscosity) of 106, is used to satisfy element incompressibility
and to provide average pressure in each element. The penalty method effectively reduces the
number of flow equations to be solved at each time step to twice the number of nodal points.
The accuracy of the penalty method for enforcing incompressibility is commensurate with the
accuracy obtained using three pressure points per element. An implicit backward time-stepping
method is employed. The temperature-dependent viscosity is determined on an element basis by
calculating the viscosity at the beginning of a time step and holding it constant over the time step.
Additional details concerning the numerical procedure are given in Schubert and Anderson
[1985].”
MC3D utilises a hybrid spectral finite difference scheme flow solver and a finite volume scheme for the
solution of the energy equation. It was originally developed at Los Alamos in the late 1980’s for
Cray/Vector architecture. and later parallelized (MPI) to run on clusters (1999). MC3D is second-order
accurate in time and space.
MILAMIN is a finite element method implementation in native MATLAB that is capable of doing one
million degrees of freedom per minute on a modern desktop computer. This includes pre-processing, solving,
and post-processing. The MILAMIN strategies and package are applicable to a broad class of problems in
Earth science. http://milamin.org/
This code was written by Jonas Ruh. It is a 2D elasto-visco-plastic FDM code.
Spectral method for modeling mantle convection with LVV has been developed. The method is stable under
high viscosity contrast (5 orders of magnitudes). Benchmarks confirm reliability of the method in
application to mantle dynamics.
The package provides tools for a range of applications in science and engineering, including second
order elliptic, parabolic and hyperbolic equations, suitable for mechanical problems dealing
with linear elasticity and for flow problems for both incompressible and compressible viscous
media.
SHELLS is a thin-shell program for modeling neotectonics of regional or global lithosphere with
faults
This code was written by B. Kaus for his phd thesis work.
SNAC (StGermaiN Analysis of Continua) is an updated Lagrangian explicit finite difference
code for modeling a finitely deforming elasto-visco-plastic solid in 3D. The code is hosted at
https://geodynamics.org/cig/software/snac/ .
STREAMV, an Eulerian, particle-in-cell, Finite Difference /Finite Volume numerical code that solves for
the conservation of mass, momentum, energy and composition for an incompressible, multi-component
viscous fluid:
To solve the momentum equation STREAMV uses a formal stream function formulation on a
staggered grid, which satisfies exactly mass conservation. Although the code is Eulerian, it
uses Lagrangian tracers for solving the advective part of the conservation of energy and the
conservation of composition with a 4th order Runge-Kutta integration scheme. This formalism easily
allows one to solve accurately Equation (6) for κci = 0 with negligible numerical diffusion. In
addition, the Lagrangian tracers can be used to calculate in real time, stirring properties or
anisotropy induced by the flow. Tracers also carry out information on material properties such
as viscosity, density, thermal expansion and thermal conductivity. This Eulerian-Lagrangian
formalism allows handling very large and sharp contrasts in material properties. For instance,
viscosity contrasts of more than five orders of magnitude across a single cell are easily handled by
STREAMV.
Not completely up to date (see website)
TEMESCH (TEmperature and Motion Equation SCHeme) is a MATLAB 2D finite difference code
developed by Valera, and others, which solves the equations of conservation of mass, momentum and energy
for an incompressible fluid. Density variations have been neglected in the motion equation except when they
are coupled to the gravitational acceleration in the buoyancy force term. Inertial forces are neglected. The
thermal effects of radiogenic heat production and adiabatic heating are included in the energy equation
whereas shear heating is neglected.
This code permits the calculation of temperature and density anomaly distributions in deep subduction
zones, taking into account self-consistently the olivine to spinel phase transformation.
The computational grid is based on a projection of the regular icosahedron onto a sphere and successive
dyadic refinements, see Baumgardner and Frederickson [107]. Concentric copies of such spherical layers of
nodes build the domain in radial direction. The first main improvement was being parallelised
Bunge and Baumgardner [265]. Particles were added in Stegman, Richards, and Baumgardner
[1983].
Baumgardner writes on his site: “As part of my Ph.D. thesis research at UCLA I developed the 3-D
spherical code now known as TERRA for modeling the dynamics of planetary mantles. This code utilized
the then newly discovered multigrid method for solving the large elliptic systems of equations arising in this
application. The efficiency of multigrid plus the advantages of the almost uniform icosahedral grid made
such 3-D calculations feasible for the first time. This code was the first 3-D spherical code of its kind and
continues almost 30 years later to be the state of the art and used by several research groups around the
world. ”
TerraFERMA is the Transparent Finite Element Rapid Model Assembler, a software system for the rapid
and reproducible construction and exploration of coupled multi-physics models.
TerraFERMA leverages three advanced open-source libraries for scientific computation that provide high
level problem description (FEniCS), composable solvers for coupled multi-physics problems (PETSc) and a
science neutral options handling system (SPuD) that allows the hierarchical management of all model
options.
TerraFERMA inherits most of its functionality from the underlying libraries but adds a layer of control
and guidance for building reusable and reproducible applications.
this category makes little sense ... should be split? removed?
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are respectively, the velocity vector,
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composition for material ’i’, chemical diffusivity of material ’i’, internal heating, and the unit vector aligned
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