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1.3.1 Advection
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advection -
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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.
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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 flux-conservative 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