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GEOL0060, Term 1 (2022):  Assessed Coursework  (25% towards the final grade)

Exercise #2

1.    Download and run Texplicit2D.m; look through the MATLAB script and familiarize yourself with it. Try to understand every step.

2.    Rewrite the MATLAB script to solve for thermal diffusion implicitly using the same model domain, resolution, Δt (i.e., timestepping) and boundary conditions.    {35%}

3.    Compare the explicit and implicit solution, for example by just sampling the solution after 20 timesteps at one point of the domain (for example (15, 17)). Repeat the comparison using different timestepping (30 timesteps using 2/3 of Δt, 25 timesteps using 4/5 of Δt, 19 timesteps using 105% of Δt, 10 timesteps using 200% of Δt [i.e., timestep twice as large as in Texplicit2D.m]). What do you conclude from this comparison?   [hint: Plot the solution as a function of timestepping to do this comparison.]     {35%}

4.    Extend the 2D implicit version of the MATLAB script such that it solves for thermal diffusion on a regular 3D mesh for 10 timesteps. The extent of the model domain and resolution in the z direction should be the same as the y direction. Visualize at least two cross sections of temperature in each dimension (one in the middle of the domain and one a bit further off-axis).

{30%}

Bonus Question (Formative Assessment):

5.    Rewrite the 2D implicit version of the MATLAB script to solve the problem with variable thermal conductivity (k). Apply different k in the plume, ambient mantle and sticky air layer. {0%}