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.

Syllabus

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:

Class rooom and time

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 2025 we will develop a model for the convection in high-pressure ice in icy ocean worlds that may controll the transfer of nutrients from the rocky interior into the ocean sandwiched between the layers of high and low pressure ice.

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For reference see [Vance at al. 2020]

Introduction

Lecture 1 (Jan 14): Course Project and Conservation Laws

Lecture 2 (Jan 16): Introduction to numerics

Lecture 3 (Jan 21): Conservative Finite Differences

1D Heat Flow

Lecture 4 (Jan 23): Discrete Operators

Lecture 5 (Jan 28): Boundary Conditions I: Dirichlet homogeneous

Lecture 6 (Jan 30): Boundary Conditions II: Dirichlet heterogenous

Lecture 7 (Feb 4): Boundary Conditons III: Neumann

Lecture 8 (Feb 6): Effective conductivity of layered media

Lecture 9 (Feb 11): Discretizing heterogenous coefficients

Lecture 10 (Feb 13): Transient heat transport - Planetesimal Thermal Evolution

1D ADVECTIVE-CONDUCTIVE HEAT TRANSFER

Lecture 11 (Feb 18): Advective heat transport

Lecture 12 (Feb 20): Time stepping ADE

DISCRETIZATION IN 2D

Lecture 13 (Feb 25): 2D Discrete operators - Part I

Lecture 14 (Feb 27): 2D Discrete operators - Part II

Lecture 15 (Mar 4): 2D Advection matrix - Cooling of oceanic plates

STOKES FLOW

Lecture 16 (Mar 6): Derivation of Stokes equation

Lecture 17 (Mar 11): Staggered grid for Stress/Strain

Lecture 18 (Mar 13): Discrete Stokes operators

Lecture 19 (Mar 25): Stokes boundary conditions & Lid-driven Cavity

Lecture 20 (Mar 27): Streamfunction

Lecture 21 (Apr 1): Coupled Stokes flow and heat transport - Mid-ocean ridges

Lecture 22 (Apr 3): Variable viscosity Stokes flow

Convection in high-pressure ices

Lecture 23 (Apr 8): Rayleigh-Bernard convection

Lecture 24 (Apr 10): Implementing convection

Lecture 25 (Apr 15): Discrete operators in spherical geometry

Lecture 26 (Apr 17): Physical properties of high pressure ices

Lecture 27 (Apr 22): Convection of high-pressure ice

Lecture 28 (Apr 24): Class review and discussion