Computing Exercises/Assignments

Labs for 2014

• Third (and final) scored lab: Lagrangian stochastic simulation of Project Prairie Grass surface layer dispersion trials. Due: Tuesday 8 April.

• Second scored lab: solving the steady-state, 2D heat equation using the relaxation method. Due: Friday 14 March.

  Instructor's solutions for lab 2: (a) using Matlab, a 3D view and a slice through y=0; and (b) using Fortran 90, slices at y=0 and y=1/8 (plotted using the free software Veusz). As the number of terms included in the analytical solution increaes to infinity, ever shorter waves (higher wavenumbers) contribute and the analytic solution captures the "peakiness" of the delta function. In the numeric solution, the equivalent progression towards the true solution is made by refining the resolution (reducing the gridlength Δ), so that the heat source, ideally a delta function (if seen in cross section through y=0, is represented by an increasingly narrow (but higher) triangle (always preserving unit area).

• First scored lab: solving the advection-diffusion equation for a gas source in the atmospheric surface layer.

  A few thoughts/reactions while marking lab 1:

  • when writing a technical report, it is implicit that your level of description should be sufficiently detailed as to allow a suitably qualified reader to repeat your work
  • diagrams can be an effective way to convey the essence of your computational problem -- e.g. the physical setup (defining axes, locating sources, sketching wind profile...), and the layout of the grid
  • as the PPG data are discrete, they ought to be represented as points, rather than lines, on your graph (the same is true in principle of model results, except that by manipulating Δz we could potentially have a very high density of points)
  • physical impact of the choice of Schmidt number S_c: when we decrease S_c we boost the eddy diffusivity, such that (at a given distance from the source) the emitted material has been mixed to higher heights. In accordance with that greater mixing, concentration near ground is reduced

• Second computational lab (slightly revised 22 Jan.) and associated flowchart (23 January; unscored). Numerical solution of the 1D heat equation.

• First computational lab (Drunkard's Walk) and associated flowchart (16 January; unscored). Programming a Drunkard's Walk simulation of dispersion in homogeneous turbulence. [File corrected 16 Jan.]

Computing exercises/assignments collected from previous years

• Best fitting the power law wind profile to wind observations
• Solve the linear advection eqn in one dimension
• Solving the non-linear advection equation
• Solving the time-dependent heat equation in one space dimension & comparison with analytical solution
• Solving the steady state heat equation in 2D
• Compute the Convectively Available Potential Energy (CAPE) from the Edmonton radiosonde (sounding) at 12Z Friday 31 July 1987 (day of the Edmonton tornado)
• Solving the advection-diffusion equation for a real world tracer gas dispersion experiment, and comparing with observations
• Spectral solution of the non-linear advection equation
• "Drunkard's walk" simulation of particle dispersion from a source in idealized turbulent flow (Random displacement model) & comparison with analytical solution
• "Drunkard's walk" simulation of particle dispersion in the atmospheric surface layer & comparison with observations
• Lagrangian stochastic simulation of gas dispersion in the atmospheric surface layer & comparison with observations
• Baroclinic weather forecast (may be selected by individuals or pairs)

Last Modified: 8 Apr., 2014