[CIG-CS] Particle problems and Semi-Lagrangian Schemes for Gamr

[Walter Landry]

Wolfgang Bangerth <bangerth at math.tamu.edu> wrote:
> 
>> > > and eliminate particles, making the code much simpler, especially in
>> > > parallel.
>> > 
>> > How would you do P-T traces with SL?
>> 
>> I am probably exposing my own ignorance, but I assume you mean
>> Pressure-Temperature,
>> or phase diagram traces so we can determine what phase is active. You
>> interpolate all the
>> fields to the point you want evaluated.
> 
> I'm with Matt for pretty much all cases, but I think there are cases
> where tracers are probably hard to avoid. Think for example if you
> wanted to keep apart a dozen different kinds of rock, i.e. the
> quantity in question is integral. Yes, we can have a field that
> starts with these integral values, but an interface between rock
> type 1 and 3 will smear out and produce rocks of kind 2 -- not what
> you probably wanted. This can only work if you have N-1 fields for N
> different phases, which might make it expensive if N is larger than
> 3 or 4.

We have to track interfaces anyway, so this is not what I worry about.

Rather, it is not clear to me how you can identify and track an
arbitrary parcel of material through its history.  For example,
consider a simulation with a single type of material.  At time 0 we
have tracers at points p0(0), p1(0), p2(0).  We take one time step and
they are now at points p0(1), p1(1), p2(1).  Another time step and
they are at p0(2), p1(2), p2(2).  At each time step, we have a place
to put the tracers' current position, pressure and temperature.  At
the end of the simulation, we can look at where the tracers end up
and examine the history of an individual tracer.  With
semi-lagrangian, there is no place to put that information.

Cheers,
Walter Landry
walter at geodynamics.org