GeoDynamo.jl

High-performance spherical-MHD solver for geodynamo and planetary-core simulations

New to GeoDynamo.jl?

Get up and running in minutes with our Getting Started guide.

What is GeoDynamo.jl?

GeoDynamo.jl is a modern Julia package for simulating magnetohydrodynamic (MHD) flows in rapidly rotating planetary interiors. It couples:

Spectral spherical-harmonic transforms via SHTnsKit
Domain-decomposed finite differences via PencilArrays
Scalable MPI parallelism for multi-node simulations

using GeoDynamo

# Configure and run a simulation
params = GeoDynamoParameters(geometry=:shell, i_N=64, i_L=31, d_E=1e-4, d_Ra=1e6)
set_parameters!(params)
state = initialize_simulation(Float64)
run_simulation!(state; t_end=0.1)

Highlights

End-to-End MHD Pipeline

Temperature, composition, velocity, and magnetic fields evolved in a single tightly coupled solver.

Hybrid Spectral-Radial Discretization

SHTnsKit for fast spherical harmonics + pencil-decomposed finite differences for radial terms.

Multiple Time Integrators

CNAB2 IMEX, exponential AB2 (EAB2), and exponential RK2 (ERK2) with Krylov-based operators.

Scalable MPI I/O

Per-rank checkpoint/output with selectable precision (Float32/Float64) and NetCDF metadata.

Boundary Topography

Linearized non-spherical CMB/ICB boundaries with Gaunt tensor mode coupling.

Architecture

┌─────────────────────────────────────────────────────────────────────────┐
│                          GeoDynamo.jl                                   │
├─────────────────────────────────────────────────────────────────────────┤
│                                                                         │
│   ┌───────────────┐   ┌───────────────┐   ┌───────────────┐            │
│   │    Fields     │   │  Parameters   │   │    Pencil     │            │
│   │  & Transforms │   │  & Config     │   │ Decomposition │            │
│   └───────┬───────┘   └───────┬───────┘   └───────┬───────┘            │
│           │                   │                   │                     │
│           └───────────────────┼───────────────────┘                     │
│                               ▼                                         │
│   ┌─────────────────────────────────────────────────────────┐          │
│   │                   Physics Kernels                        │          │
│   │  ┌─────────┐ ┌─────────┐ ┌─────────┐ ┌─────────────┐   │          │
│   │  │Velocity │ │Magnetic │ │ Thermal │ │Compositional│   │          │
│   │  └─────────┘ └─────────┘ └─────────┘ └─────────────┘   │          │
│   └─────────────────────────────────────────────────────────┘          │
│                               │                                         │
│                               ▼                                         │
│   ┌─────────────────────────────────────────────────────────┐          │
│   │              Time Integration (CNAB2/EAB2/ERK2)          │          │
│   └─────────────────────────────────────────────────────────┘          │
│                               │                                         │
│                               ▼                                         │
│   ┌─────────────────────────────────────────────────────────┐          │
│   │                  NetCDF Output & Restart                 │          │
│   └─────────────────────────────────────────────────────────┘          │
│                                                                         │
└─────────────────────────────────────────────────────────────────────────┘

Core Modules

Infrastructure

Module	Description
`fields.jl`	PencilArray-backed spectral and physical fields
`parameters.jl`	`GeoDynamoParameters` configuration management
`pencil_decomps.jl`	MPI domain decomposition via PencilArrays
`linear_algebra.jl`	Banded matrix operations for radial derivatives

SHTnsKit Integration

Module	Description
`shtnskit_transforms.jl`	Grid setup, FFT plans, transpose operators
`shtnskit_field_functions.jl`	Transforms, energy spectra, rotations

Physics

Module	Description
`velocity.jl`	Toroidal-poloidal velocity evolution
`magnetic.jl`	Magnetic field induction and diffusion
`thermal.jl`	Temperature advection-diffusion
`compositional.jl`	Composition advection-diffusion

Boundary Conditions

Module	Description
`bcs/`	Modular BC system (thermal, velocity, magnetic, composition)
`bcs/topography/`	Non-spherical CMB/ICB with Gaunt tensors

Dependencies

GeoDynamo.jl builds on a robust stack of Julia packages:

                    ┌─────────────────┐
                    │   GeoDynamo.jl  │
                    └────────┬────────┘
                             │
        ┌────────────────────┼────────────────────┐
        │                    │                    │
        ▼                    ▼                    ▼
┌───────────────┐   ┌───────────────┐   ┌───────────────┐
│   SHTnsKit    │   │ PencilArrays  │   │    MPI.jl     │
│  (Harmonics)  │   │(Decomposition)│   │  (Parallel)   │
└───────────────┘   └───────────────┘   └───────────────┘
                             │
                             ▼
                    ┌───────────────┐
                    │   NetCDF.jl   │
                    │     (I/O)     │
                    └───────────────┘

Automatic Installation

All dependencies are pulled in automatically via the package manifest. You only need a working MPI implementation and NetCDF C libraries at runtime.

Governing Equations

┌─────────────────────────────────────────────────────────────────────┐
│                                                                     │
│   ∂u/∂t  =  viscous diffusion  +  buoyancy  +  Lorentz force       │
│                     ↓                 ↓              ↓              │
│                   E∇²u            Ra·T·r̂        (∇×B)×B            │
│                                                                     │
│   ∂T/∂t  =  thermal diffusion  -  advection                        │
│                     ↓                  ↓                            │
│                (Pm/Pr)∇²T            u·∇T                           │
│                                                                     │
│   ∂B/∂t  =  magnetic diffusion  +  induction                       │
│                     ↓                  ↓                            │
│                   ∇²B              ∇×(u×B)                          │
│                                                                     │
│   Constraints:      ∇·u = 0           ∇·B = 0                      │
│                                                                     │
└─────────────────────────────────────────────────────────────────────┘

The solver advances the nondimensional Boussinesq MHD system from Sreenivasan & Kar, Phys. Rev. Fluids 3, 093801 (2018).

\[\frac{E}{\mathrm{Pm}}\frac{\partial \boldsymbol{u}}{\partial t} + (\nabla \times \boldsymbol{u}) \times \boldsymbol{u} + \hat{\boldsymbol{z}} \times \boldsymbol{u} = -\nabla p^\star + \frac{\mathrm{Pm}}{\mathrm{Pr}}\,\mathrm{Ra}\,T\,\boldsymbol{r} + (\nabla \times \boldsymbol{B}) \times \boldsymbol{B} + E \nabla^2 \boldsymbol{u}\]

Temperature & Magnetic Field

\[\frac{\partial T}{\partial t} + \boldsymbol{u} \cdot \nabla T = \frac{\mathrm{Pm}}{\mathrm{Pr}} \nabla^2 T\]

\[\frac{\partial \boldsymbol{B}}{\partial t} = \nabla \times (\boldsymbol{u} \times \boldsymbol{B}) + \nabla^2 \boldsymbol{B}\]

Constraints

\[\nabla \cdot \boldsymbol{u} = 0 \qquad \nabla \cdot \boldsymbol{B} = 0\]

Toroidal-Poloidal Decomposition

Both velocity and magnetic fields use toroidal-poloidal decomposition, which spectrally enforces the divergence-free constraints.

Documentation

Page	Description
Getting Started	Installation and first simulation
Configuration	All parameter options explained
Boundary Conditions	Velocity, magnetic, thermal, and compositional BCs
Time Integration	CNAB2, EAB2, ERK2 schemes
Spherical Harmonics	SHTnsKit transforms and operators
Boundary Topography	Non-spherical boundary coupling
Data Output	NetCDF files, restarts, diagnostics
Developer Guide	Contributing and code structure
API Reference	Complete function documentation

Compatibility

Environment	Versions	Status
Julia	1.10, 1.11	Supported
Linux	OpenMPI, MPICH	Tested in CI
macOS	MPICH (Homebrew)	Tested in CI
Windows	Microsoft MPI	Tested in CI

Citation

If GeoDynamo.jl supports your research, please cite:

@software{geodynamo_jl,
  author = {Kar, Subhajit},
  title  = {GeoDynamo.jl: Spherical-MHD Solver for Planetary Cores},
  url    = {https://github.com/subhk/GeoDynamo.jl},
  year   = {2024}
}

Get Involved

Community feedback via GitHub Issues and PRs is the fastest way to expand physics modules and add diagnostic hooks!