CRPIT = Controlled Remeshing with Partial Interface Tracking

CRPIT was developed to deal with specific types of salt models. The early evolution of these particular models, in which the salt interface is tracked by the Eulerian mesh, worked well.

Later, on a restart, the Eulerian tracking of the interface was abandoned. The restart was fine but the Eulerian mesh retained a character that reflected the earlier phase of interface tracking (i.e. it was not a good mesh for the later calculations once the interface tracking was abandoned). A method was needed to restore the Eulerian mesh to a better configuration.

In addition, the salt models evolved diachronously, such that interface tracking should have been used in the distal parts of the system after it had been abandoned in the proximal parts.

CRPIT (Controlled Remeshing with Partial Interface Tracking) was developed as a partial solution to these problems.

The idea of CRPIT is very simple: the Eulerian interface that corresponds to the top of the salt (or any other interface) is 'tracked' but the way it moves vertically is determined by an operator function f(x,t) -- the Control function.

The Eulerian interface is still designated as one that is selected to be tracked, i.e. interface tracking is not abandoned, it just works in a different way.

Let z = T(x) be the position of the tracked Eulerian interface

Let z = TA(x) be a target function, the position we want to move T(x) to once tracking of the interface to align it with the salt has been 'abandoned'

That is, this method tracks the Eulerian interface where it makes good sense, but adopts a different strategy where the interface is no longer to be tracked.

f(x,t) has 4 regions/intervals:

1) Move interface progressively closer to the specified target position.

In the interval x < x1, abs[f(x,t)] is a fraction which specifies the proportion of the distance between T(x) and TA(x) that T(x) will be moved by remeshing for this timestep. That is, T(x) will be moved by delta(T(x)) where delta(T(x)) = abs[f(x,t)]*(T(x)- TA(x)).

f(x,t) should chosen to be small, e.g. 0.01 so that T(x) migrates slowly toward to TA(x). Note that f(x,t) is negative in Region 1.

Currently, TA(x) is a constant. In later versions, it may vary with x but should always be above or below T(x) so that even a constant value of f(x,t) will cause T(x) to converge on TA(x).

2) In interval x1 <= x < x2, f(x,t) decreases monotonically to 0 at x2. This means that as x increases between x1 and x2, the rate at which T(x) converges on TA(x) decreases to 0, i.e. at x2 the remeshing does not move T(x).

3) In interval x2 <= x < x3, f(x,t) increases monotonically from 0 to 1.0. In this region the remeshing tracks the Eulerian interface imperfectly, i.e. the tracking is scaled by f(x,t) and therefore only 'tracks' the interface by the true displacement multiplied by f(x,t).

4) Full tracking of the Eulerian interface

In interval x3 <= x, f(x,t) has the value 1.0. In this region the Eulerian interface is fully tracked during remeshing. Note that "fully tracked" is imperfect because the remeshing only adjusts the Eulerian mesh vertically whereas the nodal velocities/ displacements are both horizontal and vertical.

Time Variation of f(x,t)

f(x,t) can be specified to move spatially with velocity vf. (Currently, this is a constant but could be vf(t).)

This allows the diachronous behaviour of salt models to be included by moving f(x,t) such that:

Region 1 is positioned where tracking of the salt interface has been abandoned and the aim is to progressively restore the Eulerian mesh to a 'good' configuration.

Region 4 is the region of full tracking of the Eulerian interface

Regions 2 and 3 allow interpolation between the 'goals' of Regions 1 and 4. These regions should be sufficiently wide to prevent strong distortion of the Eulerian mesh because the 'goals' of regions 1 and 4 may cause remeshing in which the remeshed interface is moved in opposite directions.

This page was last modified on Tuesday, 17-Aug-2010 13:16:09 ADT
Comments to geodynam at dal dot ca