New subject: upwind example remark; extension to CN in time

26 Jun 2016

      D+ and D- refer to the values either side of an interior facet between two
cells.

On the boundary (exterior facets), there is no such ambiguity, so just D is
used.

In the steady-state example on the website, this D enters the
left-hand-side integral over the outflow part of the boundary, while the
prescribed function D0 is used in the integral over the inflow part.

"In general", you can write a term that contains both D and D0 and 'picks
the right one' depending on the sign of u.n (this is how the interior facet
integral works).  Note that n always points *outwards* on the exterior
boundary facets.

On 26 June 2016 at 12:24, Onno Bokhove <O.Bokhove@leeds.ac.uk> wrote:
...
The issue is that D_('+') (or D_('-')) is not defined but I don't
understand why not, or how to fix it?
------------------------------
*From:* firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk>
on behalf of Onno Bokhove <O.Bokhove@leeds.ac.uk>
*Sent:* Sunday, June 26, 2016 12:21 PM
*To:* firedrake
*Subject:* Re: [firedrake] upwind example remark; extension to CN in time
Yes that was my point indeed.
To build any more advanced code upon this one, one
would need to use an alternate approach entirely
through the flux.
That is why it may be useful to extend the
example with two alternatives: the simple one shown
and one flux-based only.
By the way, in the attached I have L2=0 and thet=0;
if I uncomment the actual L2 there is a complaint,
even though they=0.
Obviously I need this term for the general theta-scheme,
including thet=0.5 (Crank-Nicolson).
I am doing the above simple extensions to get used to FD!
Small steps ...
The example is ties such that value 1 advects into through the
entire domain in the time set.
------------------------------
*From:* firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk>
on behalf of Colin Cotter <colin.cotter@imperial.ac.uk>
*Sent:* Sunday, June 26, 2016 11:26 AM
*To:* firedrake
*Subject:* Re: [firedrake] upwind example remark; extension to CN in time
Hi Onno,
  In answer to your first question. Things are simplified in the advection
demo because we know which edges are upwind, which are downwind, and which
have no flow through them. If you wanted to generalise this, then we would
need a surface integral over the entire external boundary with a switch
that either gave the internal value of the tracer or the inflow boundary
condition, depending on the direction of u.n, just like we did for the
interior facets.
Instead, in this example, on the outflow boundary we just write an
integral involving the interior value, and on the inflow boundary we write
an integral setting the inflow values.
all the best
-cjc
On 25 June 2016 at 16:05, Onno Bokhove <O.Bokhove@leeds.ac.uk> wrote:
...
Hi FDs,
(i) The upwind example is odd in that the real boundaries are treated
in a special way rather than setting the outside value in
the same numerical flux as anywhere else;
my question is how this can be fixed?
So no special terms at the in- and outflow, just specify
the outside velocity used. This is imo the proper DG way not was is done
now.
(ii) Attached my attempt to do a time dependent advection
with Crank Nicolson, which works but does not yet
give the right answer, in part due to (i).
[I don't understand why I have to make
my theta variable that a constant but other wise it did not work.]
Any suggestions, corrections, also on other silly things done by me?
Next step is to extend to system with 3 equations;
hence the few extra but unused variables.
Thanks, from midnight Seoul in old style Korean guesthouse.
Onno
------------------------------
--
http://www.imperial.ac.uk/people/colin.cotter
www.cambridge.org/9781107663916

Re: [firedrake] upwind example remark; extension to CN in time

Andrew McRae

Onno Bokhove

tags

participants (2)