Introduction to scientific programming in Earth's Sciences

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Introduction to scientific programming in Earth's
Sciences
J.W. Goethe University. Frankfurt

• Dr Guillaume RICHARD
• Institüt für Geowissenchaften 1.232
• richard_at_geophysik.uni-frankfurt.de

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Overview

• 12 x 45min Lectures / 45min training classes
  (praktical)
• Basics (Hardware, OS, editor, etc.. )
• Basics 2 (Linux commands, Compile,Visualize )
• Languages Fortran (FORmula TRANslation)
• Languages Fortran (2)
• Languages Fortran (3)
• Languages Fortran (4)
• Languages C/C
• Languages Matlab (1)
• Languages Matlab (2)
• Languages Introduction to Maple
• Introduction to Finite difference method
• A study case Solving the heat equation in 1D

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L. 12 A study Case The heat equation in 1
Dimension
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The Problem
A hot diapir emplaced at the base of the crust.
How long does it take for the temperature to come
back to steady state ?
Schematic illustration showing a possible model
to explain the development of Hall-Star Chrome
type orenbodies in the middle-upper crust.
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And now ?
1. Problem. Clearly and unambiguously identify
the problem to be solved.
Remember lesson number 1
1D Heat diffusion equation with a constant
diffusivity K
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The Model

• Approximations
• Settings
• Boundary conditions
• Initial conditions

1-Dimensional model Constant diffusivity K
Solve only for the crust fixed
Temperature Adiabatic profile
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The Method

• Use of
• Fortran90 language
• Finite difference method
• Explicite in time numerical scheme

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Implementation

• Define a grid
• What are the necessary variables to define ?
• Lets write this code !

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Assessment
Analytical solution Using similarity approach it
is possible to show (Turcotte Schubert,
Geodynamics, 2002, p153-157) that a analytical
solution to the diffusion equation is given by
(for specific BCs !)
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Assessment
Analytical solution In our case fixed Temperature
Boundary conditions (BCs). We can find a solution
using variables separation
Where the constants Cs can be calculated
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Visualisation
Matlab Load the data into Matlab and plot it (T
as function of x for different time.) Tecplot Load
the data into Tecplot and plot it