This repo contains jupyter notebooks implementing solutions to selected problems from Taras Gerya's Introduction to Numerical Geodynamic Modeling in the Julia programming language.

These exercises were assigned to students as part of a graduate level GEL298 course at UC Davis, Winter 2022. If you find mistakes or you find this useful and wish to discuss, please send me an email!

Chapter-01-02-Divergence-EOS.ipynb

1. Computation of material properties (density, thermal expansivity, compressibility) using finite differences.
2. Plot a vector velocity field and its divergence in 2D.

Chapter03-PoissonEquation.ipynb

1. Solve the Poisson equation in 1D and compare the numerical solution with an analytic solution.
2. Solve the poisson equation in 2D cartesian coordinates using a 5-point stencil.
3. Use ML and GMRES to solve the poisson equation with a geometric multigrid preconditioner.

Chapter05-StokesEquations.ipynb

• Solve the Stokes equations with constant viscosity using a vorticity-stream function approach in 2D Cartesian coordinates.

Chapter07-NumericalStokes.ipynb

• Solve the Stokes equations with variable viscosity in 2D Cartesian coordinates.

Chapter08-Stokes-Continuity-Markers.ipynb

• Solve the Stokes equations with variable viscosity and advect density and viscosity using markers.

Chapter10-HeatEquation.ipynb

• Solve the heat conduction equation.

Chapter11-I2VIS.ipynb

• Solve the coupled Stokes and energy equations in 2D.
• Advect temperature using markers.
• Use a cell-centered discretization for the temperature equation.
• This functionality is similar to the code I2VIS (Gerya and Yuen, 2003).

Chapter13-I2ELVIS.ipynb

• Include the ability to model the deformation of a viscoelastic material.
• This functionality is similar to the code I2ELVIS (Gerya and Yuen, 2007).
• This notebook hasn't been finished/

Chapter18-PoissonMultigrid.ipynb

• Solution of a Poisson problem using multigrid. The implementation here loosely follows what is described in Gerya's book.

Additional Notebooks:

There are some additional notebooks written to demonstrate solutions in curvilinear coordinates and on unusual grids, such as the overset yin-yang grid.

M01-Spherical-Annulus-Poisson.ipynb

• Solve the poisson equation in the 2D spherical annulus.

M02-SphericalAnnulus-StreamFunction.ipynb

• (work in progress) solve the stokes equation in the 2D spherical annulus using a stremfunction approach.

M03-Poisson_3D.ipynb

• Solve the Poisson equation in 3D using a multigrid smoother.

M04-YinYang.ipynb

• Solution of a Poisson problem on a spherical surface using an overset grid, called the yin-yang grid, described in Kageyama and Sato (2004). The point of this problem was to think about how to set up the constraint equations and indexing for a code like StagYY. It is guaranteed to be far from optimal and the disretization doesn't appear to be well-suited to the use of iterative solvers.