AMME5202 Assignment 1: Advection and Diffusion
Due: 5pm Friday, Week 7 (10/04/2020)
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This assignment should take a typical student 30 hours to complete.
In this assignment we will consider the two-dimensional advection diffusion equation for a
scalar σ(x; y; t). All quantities are non-dimensional.
@tσ + u@xσ + v@yσ = κ (@x@xσ + @y@yσ) :
You can imagine this represents any scalar quantity such as temperature or salt concentration. The diffusivity is κ = 1 × 10-4 and the initial condition is,
σ(x; y; 0) = 0:0:
The domain is a unit square,
-0:5 < x < 0:5 and – 0:5 < y < 0:5:
The velocity field inside the domain is,
u = 0:04 and v = 0:01:
A Dirichlet boundary condition is set on the x = -0:5 boundary
σ(-0:5; y; t) = exp -500 · (-0:125 – y)2;
with all other boundaries zero normal gradient,
@x
σ(0:5; y; t) = 0; @yσ(x; -0:5; t) = 0 and @yσ(x; 0:5; t) = 0:
The aim of the a
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