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

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 2023 we will develop a model for hydrothermal convection in porous media. This has applications to several research problems, including the post impact hydrothermal evolution of the Chicxulub crater and the minig of elements from the silicate interior of asteroisd and moons, in particular Jupiter’s moon Europa.

Introduction

Lecture 1 (Jan 10): Course Project and Conservation Laws

Lecture 2 (Jan 12): Balance laws

Lecture 3 (Jan 17): Introduction to numerics

1D Numerics - Poisson Equation

Lecture 4 (Jan 19): Discrete Operators

Lecture 5 (Jan 24): Shallow Aquifer Model

Lecture 6 (Jan 26): Dirichlet Boundary Conditions

Lecture 7 (Jan 31): Effective conductivity of layered media

Lecture 8 (Feb 2): Discretizing heterogenous coefficients

Lecture 9 (Feb 7): Fluxes and Flux Boundary condition

Lecture 10 (Feb 14): Radial coordinate systems

2D Numerics - Poisson Equation

Lecture 11 (Feb 16): 2D Discrete operators - Part I

Lecture 12 (Feb 21): 2D Discrete operators - Part II

Lecture 13 (Feb 23): Streamlines and Streamfunction

Lecture 14 (Feb 28): Numerical Streamfunction

Heat transport (Advection-Diffusion Equation)

Lecture 15 (Mar 2): Energy Conservation

Lecture 16 (Mar 7): Steady conduction

Lecture 17 (Mar 9): Heat equation & timestepping

Spring Break (Mar 14 & 16)

Lecture 18 (Mar 21): Transient heat conduction - finite

Lecture 19 (Mar 23): Transient heat conduction - infinite

Lecture 20 (Mar 30): Advection equation & advection operator

Lecture 21 (Apr 4): Transient Advection-Diffusion

Lecture 22 (Apr 6): Advection operator 2D

Lecture 23 (Apr 11): Convection - equations

Lecture 24 (Apr 13): Porous flow with gravity

Lecture 25 (Apr 18): Convection - numerics

Lecture 26 (Apr 20): Discussion