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1.3.1 Advection
Slide : [
advection 
waves 
VIDEO
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Also called convection, advection models the streaming of
infinitesimal elements in a fluid. It generally appears when a transport
process is modeled in a Eulerian representation using the convective
derivative

(1.3.1#eq.1) 
For a constant advection velocity
, the advection equation can be
solved analytically
,
showing explicitly the underlying characteristic
.
Try the JBONE applet
below
to compute the advection of a Gaussian pulse using the Lagrangian CIP
method from chapter 6.
JBONE applet: press Start/Stop
to simulate the advection of a Gaussian pulse.
Verify that the pulse indeed propagates with an advection velocity
u=1 as chosen in the input parameters.

Both experiments show that numerical simulations have to be used carefully,
to work withing limits of applicability that will be discussed in the
comming sections.
Note that for a constant advection speed, the wave equation can be written
in fluxconservative form that reminds an advection

(1.3.1#eq.2) 
This shows explicitly that the numerical methods for the advection
equation can in principle be used also for wave problems.
SYLLABUS Previous: 1.3 Prototype problems
Up: 1.3 Prototype problems
Next: 1.3.2 Diffusion
