Aug. 17, 2004 Klaus Hallatschek and Dorland have a recent paper (2004-2003?) looking at collisional and passing particle effects on particle transport, for edge parameters. They found cases where they need a really small time step and high k_x, for cases where collisions are strong, to get particle transport accurately (they needed nu*dt=0.05.). For such cases, a less-split version of collisions, or a Krylov iterative solver, might improve things. Subject: Re: gs2 bakdif=0.05 Date: Thu, 29 Mar 2001 20:28:42 -0500 From: Bill Dorland Reply-To: bdorland@ipr.umd.edu To: hammett@pppl.gov, dernst@pppl.gov, cbourdelle@pppl.gov On a couple of occasions, I have checked that results are independent of bakdif, for 0 < bakdif < 1, as long as the eigenfunction can be resolved and for small enough time step (a standard constraint). I run almost always with bakdif = 0.05. Greg had concerns similar to Darin's (as I recall) a while back and so used a value of zero in his template, but I haven't run with zero in ages. The problems that bakdif solves are related to small v_parallel. Mike K. had a clear reason for introducing it (soon after the KRT paper was written), but I don't have notes on this handy. When up-down asymmetry is allowed, it is sometimes necessary to use larger values of bakdif, of order 0.3. I can explain how this parameter enters the differencing scheme if anyone is really interested, but I'd prefer to do it after Sherwood. --Bill Subject: Re: gs2 bakdif=0.05 Date: Thu, 29 Mar 2001 20:12:33 -0500 From: Greg Hammett Organization: Princeton University Plasma Physics Laboratory To: Darin Ernst CC: bdorland@ipr.umd.edu, cbourdelle@pppl.gov Darin, Thanks for thinking about this. I think this is okay, but there are lots of things that could be investigated further. This is a parameter that affects spatial differencing. It doesn't affect time differencing per se (the amount of "implicitness/explicitness" or centeredness). Kotschenreuther's spatial differencing algorithm is a little unusual (see the KRT paper for a description of it). It is elegant because it preserves 2cd order spatial differencing, and preserves a nice symmetry between the way space and time are differenced (in an equation df/dt + df/dx=C, it would appear that t and x should be differenced in equivalent ways). But it causes the coefficient of the d/dt operator to vanish for modes at the grid Nyquest wave number. I.e., in an equation for df/dt in the middle of p. 3 of my notes at http://w3.pppl.gov/~hammett/work/gs2/docs/implicit.ps there is a term cos(k Delta z/2), which vanishes at the Nyquist wave number. I don't fully know what effect that has on the numerics, some day it should probably be investigated further. If the eigenfunction (vs. theta) is well resolved and smooth, then this shouldn't matter, but perhaps in some cases doing a little upwind differencing helps keep things better-behaved at the barely-resolved scales. I think bakdif=0.05 should be okay, but perhaps it would be useful to check another case that works okay with bakdif=0 and verify that the results don't change much when bakdif is changed to 0.05. I think it would be equivalent to adding a little bit of collisional damping. Presumably another option should be to increase the theta resolution? Another alternative to investigate some day might be a 3rd order upwind differencing algorithm. This would have little effect on the well resolved modes, and introduce some dissipation only into the shortest scales... I think it could be solved implicitly just about as efficiently as the present algorithm. Perhaps it would be useful to put a diagnostic into GS2 that looked at the wiggles in the eigenfunction vs. theta and warned the user if it didn't look converged. Thanks, Greg