GEO 325M/398M Numerical Modeling in the Geosciences

Jackson School of Geosciences - University of Texas at Austin

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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