GEO 325M/398M Numerical Modeling in the Geosciences

Jackson School of Geosciences - University of Texas at Austin

Project maintained by mhesse Hosted on GitHub Pages — Theme by mattgraham

Course Description

Covers numerical solution of dynamical problems arising in the solid earth geosciences. Entails development of individual codes in Matlab and application of codes to understanding heat transfer, wave propagation, elastic, and viscous deformations. Requires familiarity with Matlab.

Previous course projects:

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The course content will be guided by a current research problem that typically leads to a scientific publication within the following year. In past classes we have worked on the following problems:

Office hours


Mon 4-5pm and Wed 4-5pm: Zoom ID 983 3529 1432 (password in email or on Canvas)

Additional course websites:

Matlab basics:

Here are some LiveScripts I prepared for the first class in 2018 that didn’t have a Matlab prerequisite. If you don’t have much Matlab experience, please look through them. Vectorized programming is a particularly important topic.

  1. demo_arrays.mlx [pdf]
  2. demo_functions.mlx [pdf]
  3. demo_control_flow.mlx [pdf]
  4. demo_matlab_functions.mlx [pdf]
  5. demo_plotting.mlx [pdf]
  6. demo_vectorized_programing.mlx [pdf]
  7. demo_odds_ends.mlx [pdf] (structures, logical indexing, anonymous functions)

Below are two files that I have sometimes used for the demos in class. If you put them into the folder with class files you should have no problem.

This years course project

In spring 2022 we will develop a model for two-phase convection in Europa’s ice shell. Europa is one of the Galilean moons of Jupiter. Tidal heating due to Jupiter’s gravity leads to melting and the persistence of an internal ocean that might harbor life [Nasa video]. This year we will explore the effect of tidal heating on Europa’s ice shell, where it leads to partial melting and the formation of a dense brine. This leads to complex two-phase (Darcy-Stokes) convection where warm buoyant ice rises and dense brine percolates downwards. To date these dynamics are largely unexplored but have the potential to dramatically thin the ice shell and hence our ability to probe the internal ocean.

1D Numerics - Poisson Equation

Lecture 1 (Jan 18): Course Project and Conservation Laws

Lecture 2 (Jan 20): Balance laws

Lecture 3 (Jan 25): Introduction to numerics

Lecture 4 (Jan 27): Discrete Operators

Lecture 5 (Feb 1): Shallow Aquifer Models

Lecture 6 (Feb 3): Dirichlet Boundary Conditions

Lecture 7 (Feb 8): Effective conductivity of layered media

Lecture 8 (Feb 10): Discretizing heterogenous coefficients

Lecture 9 (Feb 15): Fluxes and Flux Boundary condition

1D Melt migration (simplified)

Lecture 10 (Feb 17): Melt migration intro

Lecture 11 (Feb 22): Scaling melt migration equations

Lecture 12 (Feb 24): Solving the flow problem

Lecture 13 (Mar 1): Transport problem - advection equation

Lecture 14 (Mar 3): Transport problem - time stepping

2D Numerics

Lecture 15 (Mar 8): 2D Discrete operators - Part I (Traveling - zoom lecture!)

Lecture 16 (Mar 10): 2D Discrete operators - Part II (Traveling - zoom lecture!)

No class Mar 15 and 17 (Spring break)

Lecture 17 (Mar 22): 2D Discrete Advection

Stokes equation

Lecture 18 (Mar 24): Navier-Stokes equation

Lecture 19 (Mar 29): Stokes equation

Lecture 20 (Mar 31): Stokes grid

Lecture 21 (Apr 5): Stokes operators

Lecture 22 (Apr 7): Stokes boundary conditions

Lecture 23 (Apr 13): Streamfunction

Lecture 24 (Apr 15): Variable viscosity Stokes flow

Lecture 25 (Apr 20): Discretization with variable viscosity

Melt migration (Darcy-Stokes)

Lecture 26 (Apr 26): Derivation of Darcy-Stokes equations I

Lecture 27 (Apr 28): Derivation of Darcy-Stokes equations II

Lecture 28 (May 3): Head formulation for Darcy-Stokes equations

Lecture 29 (May 5): Discretization of Darcy-Stokes