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 or two. 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 2024 we will develop a model for infiltration of rain water. We will start from the standard description of unsaturated flow given by Richards’ equations. From there we can explore several extensions depending on time available. Options are: 1) Flow of soil gas, 2) Freezing and thawing soild, 3) Preferrential flow.

Introduction

Lecture 1 (Jan 16): Course Project and Conservation Laws

Lecture 2 (Jan 18): Balance laws

Lecture 3 (Jan 23): Introduction to numerics

Lecture 4 (Jan 25): Conservative Finite Differences

1D Saturated Flow (Poisson Equation)

Lecture 5 (Jan 30): Discrete Operators

Lecture 6 (Feb 1): Shallow Aquifer Model

Lecture 7 (Feb 6): Dirichlet Boundary Conditions

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

Lecture 9 (Feb 13): Discretizing heterogenous coefficients

Lecture 10 (Feb 15): Fluxes and Flux Boundary condition

2D Saturated flow

Lecture 11 (Feb 20): 2D Discrete operators - Part I

Lecture 12 (Feb 22): 2D Discrete operators - Part II

Lecture 13 (Feb 27): Streamlines and Streamfunction

Lecture 14 (Feb 29): Numerical Streamfunction

Lecture 15 (Mar 5): Correlated Random Fields

Lecture 16 (Mar 7): Solute Transport

Lecture 17 (Mar 19): Transient Diffusion

Lecture 18 (Mar 21): Time integration

Lecture 19 (Mar 26): Advection equation

Lecture 20 (Mar 28): 1D Advection operator

Lecture 21 (Apr 2): 2D Advection operator

Unsaturated flow

Lecture 22 (Apr 4): Richards equation

Lecture 23 (Apr 9): Capillary diffusion

Lecture 24 (Apr 11): Fully-coupled solution

Lecture 25 (Apr 16): Newton’s Method with Analytical Jacobian

Lecture 26 (Apr 18): Gravity driven infiltration

Lecture 27 (Apr 23): Solving non-linear advection

Lecture 28 (Apr 25): Solving full Richards Equation