channelflow.org

====== Differences ====== This shows you the differences between two versions of the page.

--- gtspring2009:gibson:misc [2009/07/18 17:51]
gibson
+++ gtspring2009:gibson:misc [2010/02/15 13:33] (current)
gibson
@@ Line 1: / Line 1: @@
 on which I post my miscellaneous daily activities
-===== to-do list=====
+===== to do =====
-  - Produce Poincare section plots for EQ2 unstable manifold and P47p18. 1 day. 2009-07-16
+  - Apply for funding for Channelflow. PC 2009-11-30
-  - Add functionality to DNS to terminate integration on a Poincare section. 1 or 2 days. 2009-07-16
+  - Get a job a year hence. 2009-11-03
-  - Review a PRE.  2009-07-16
+  - Write periodic orbit paper. 2009-08-25
-  - Read/edit proof of n00bs.  2009-07-16
+  - Write 2d navier-stokes integrator. 2009-08-25
-  - Respond to queries about forcing functions in channelflow howto blog.  2009-07-16.
+  - Cylinder wake. 2010-02-15
-  - Figure out why I can't converge past 1e-05 for traveling waves in x. Gotta be a bug.  2009-07-17
+  - Localized plane Couette solutions, JFM paper. 2010-02-15
-  - Write out idea for near-wall solutions. 2009-07-18.
-===== have-done list=====
+===== am doing =====
-  - Write an ad-hoc program to translate localized solutions so they're s_xyz-symmetric about the center of the box. Took a whole day, longer than I thought. 2009-07-17
-  - Center the snaking-bifurcation solutions and compute their eigenspectra. Done 2009-07-18.
-===== unstable periodic orbits - University College of London =====
+-11-03
+  * Good news: The "Spots, Stripes, and Turbulence" symposium was accepted for the March APS meeting. This was organized by Tobias Schneider, John Burke, and me. Also I was invited by Jean-Philippe Lessard and Konstantin Mischaikow to speak at the Eastern Regional meeting of the AMS in May.
+  * While writing up the Poincare-section method of generating initial guesses for periodic orbits, I realized that it greatly simplifies the generation of initial guesses for relative periodic orbits as well. Since time is discrete, choosing the initial guess for phase is a 2d or 1d search, depending on the symmetry of the velocity. So I have started a number of RPO searches; assuming that goes well we will have POs and RPOs for this paper.
+  * Entered channelflow in [[http://www.dynamicalsystems.org/sw/sw/list|dynamical systems software list]].
+  * Am combing through job announcements. It ain't pretty.
+-11-01 PC: John, you might want to enter Channelflow.org into [[http://www.dynamicalsystems.org/sw/sw/list|dynamical systems software list]]. November already. Mein Gott.
--06-30 JFG: This page was world-readable, but I changed it to GTspring09-only. Agreed about Boghosian. I heard him talk about linear algebra algorithms on the Connection Machine when I was at los Alamos. I have the sinking feeling that Jonathan mentioned after reading Smeigel's thesis.... Lattice-Boltzmann is sub-optimal way to simulate Navier-Stokes, I think. Good for parellization, bad for discretization. I wonder if their solutions converge. This would seem to prove you right that is is computationally feasible to compute orbits variationally, in a spatio-temporally discretized search space. I should have been clearer in my earlier protestations that it was not feasible for //me// to do it in a time scale that either of us would be comfortable with.
+-10-20 PC: would be nice to do a man-to-man skype about weltanschanung in general. Click on skype if I show up green
--06-29. PC: this info is confidential, so I am putting it on a password protected page - move it wherever else you see fit, as long as it is not world-readable.
+-10-16 Localized EQB/TW PRL largely in place. Figures are done, the text is in place but needs to be shrunk. References are not done.  I am headed to California for a week and two weekends with Uma, to visit my sister and
-Here is a talk that will be presented in Trieste end of July (I remember Boghosian as a smart guy):
+attend a wedding. Will be back 2009-10-27. Will be in email contact but only sporadic nighttime skype.
-Author(s): L. Fazendeiro$^1$, B. M. Boghosian$^2$, P. V. Coveney$^1$, J. L{\"{a}}tt$^3$, S. Smith$^2$\\
+Periodic orbit paper:
-Affiliation(s): $^1$ Centre for Computational Science, University College of London, 20 Gordon Street, London WC1H 0AJ, UK; $^2$ Department of Mathematics, Tufts University Bromfield-Pearson Hall, Medford, MA 02155, U.S.A.\\ $^3$ Institute of Mechanical Engineering, Ecole Polytechnique Federale de Lausanne CH-1015 Lausanne, Switzerland}\\
+  - Thirtyish S-symmetric orbits: an IvD plot of a few of them at HKW Re=400, table of properties, movies.
-Email(s): l.fazendeiro@ucl.ac.uk, bruce.boghosian@tufts.edu, P.V.Coveney@ucl.ac.uk, jonas.latt@gmail.com, Spencer.Smith@tufts.edu\\
+  - Methods: computation of Poincare intersections, generation of initial guesses from close returns on I-D=0 Poincare section, restriction of time integration to symmetric subspace
-Position(s) of author(s)/presenter(s): PhD student (presenter/first author)
+  - Dynamics: one of
+       * an initial stab at linearization about P-section FPs, see how large the region of accurate linearization is,
+       * possibly extend unstable manifold of an orbit or two and look for heteroclinic connection between two orbits.
+       * symbolic dynamics via Voronoy triangulation or spheres around FPs, based on the estimate of linear accuracy.
-Abstract text: "We present a novel algorithm for the identification of periodic orbits in differential equations. With this new approach, both space and time are parallelized, and a search procedure minimizes a functional simultaneously towards the trajectory of the orbit in phase space and its period. We discuss in detail the methodology followed for the identification of unstable periodic orbits (UPOs) in the Navier-Stokes equations (NSE) for incompressible viscous fluid flow, simulated using the lattice Boltzmann method.
-It has been known for quite some time that driven dissipative systems exhibit finite-dimensional attractors which are replete with UPOs. The attractors can be thought of as the closure of the set of all such UPOs. The UPOs in turn provide a countable sequence of trajectories from which dynamical averages can be extracted using the zeta function formalism. Averages thus obtained are not stochastic in nature, i.e., they do not suffer from the problem of having the statistical error decay as the inverse square root of the number of decorrelation times. In this presentation we discuss the numerical difficulties involved in the numerical relaxion procedure for systems with very many dimensions such as the NSE, and describe the application of the conjugate gradient method to the problem. Since this method requires the storage in memory of spacetime trajectories, huge computational resources are required, which places the work firmly in the emerging field of petascale grid computing. We present results obtained on the IBM BlueGene/P at the Argonne National Laboratory and on the Sun Constellation Linux Cluster at the Texas Advanced Computing Centre, two of the world's current largest resources for open science. Results of turbulent flow simulations are presented and discussed and preliminary periodic orbits are presented. The insights that the identification and classification of these UPOs are expected to bring to turbulence theories are discussed.
-===== localized eqbs =====
+-10-10 Wrote out idea for near-wall solutions.
+-10-06 Have 31 HKW orbits at I-D=0 and at 48x33x48 (32x33x32 after dealiasing) dt~0.03, most confirmed to be 1e-04 or 1e-05 accurate at 64x49x64 and dt~0.02 and to converge quickly at that resolution. A few of the longer orbits are perhaps spurious at the low resolution, with initial error 1e-02 or 1e-03 and slower initial convergence. Will have to compare IvD plots at the two resolutions. Next step: try linearization about a specific orbit, or extend unstable manifold within Poincare section.
+-10-05 Organizing orbits for plotting, posting, writing up: scping from PACE, getting to same gridsize, choosing best Poincare intersection, computing trajectories, plotting I vs D, etc.
+-10-05 Found ten new HKW orbits since last Thursday using close recurrences on I-D=0 Poincare section for initial guesses. It is so much easier this way. I think a JFM paper describing this, presenting a table of the thirtyish orbits, showing a few in detail, and perhaps a section showing how unstable manifolds of the return map can be continued in the Poincare section, would be a good paper. Also, some [[gtspring2009:gibson:localsolns#section21|interesting new results]] on continuation in streamwise length for the localized solutions.
+-09-25 Localized PCF PRL is underway. Continuing existing orbits in aspect ratio, diagonal length, and Reynolds using I-D=0 Poincare section.
+===== have done =====
+"have done" is just "am doing" suitably aged
+-11-30 **Laurette**, via **PC**: I was very nice to you guys? I'd say it was the other way around!
+  - I used one of the channelflow figures to illustrate perfectly the minimal flow unit
+  - I used the Gibson laptop to give my presentation with movie (which my own computer was incapable of doing)
+-11-30 **PC** to **Laurette**: John reports you were very nice to us humbldt plumbers in your talk - mercy buckets!
+-11-25 We got **a lot** of love at the APS meeting: mentions in many talks, including a prominent placement in Laurette's invited session (she placed us along with Wedin, Kerswell, Eckhardt, Faisst, Hof and others in a line of progression starting with Reynolds) plus a enthusiastic recommendation of channelflow.org. A number of people came up to me and thanked me for channelflow.org and/or spoke highly of our first JFM paper. And the localized solution work made a big impact. We really got a lot of excitement over that.
+-09-15 Um, a couple weeks went by there. Have started localized eqb paper w Tobias and John Burke (for PRL). Set up
+using subversion hosting on svn.channelflow.org to avoid ssh tunneling problems and need for GT accounts. Long discussion
+w Wally and Divakar about whether transition to turbulence in large (8pi x 2 x 8pi) domains results from close passes to Nagata-Busse-Clever-Waleffe LB EQBs. Found no evidence supporting this idea. Resumed continuations in Re of HKW orbits, using I-D=0 Poincare section to eliminate temporal phase shifts. This improves the quadratic extrapolation in the continuation parameter and reduces the amount of manual oversight needed in continuations. Am just focusing on continuing a few orbits for the PO paper to demonstrate parametric robustness of orbits and a few connections via bifurcation.
+-08-25 Set up skeleton for localized PCF PRL paper on svn.channelflow.org; thankless professional activity.
+-08-24 Nailed down saddle-node bifurcation of localized EQB in 4pi,16pi box. Eigenfunction has expected shape (concentrated near edges of solution); another eigenvalue crossing the imaginary axis shortly after bifurcation could give rise to EQB-TW connections.
+-08-20 Figuring out the symmetries of the EQB and TW bifurcations. It is amazing how much time stuff like this takes, getting all the solutions in compatible spatial phases, figuring out the symmetry groups on the larger domains, calculating eigenfunctions and their symmetries...
+-08-19 The calculations of I-D=0 intersection of all the HKW orbits should be done today. While those are going on I'm going to see if I can figure out the symmetries of bifurcations of the localized EQB and TW off the globally periodic solution, in prep for a Friday meeting with Tobias and John.
+-08-18 Calculating intersections of HKW orbits with I-D=0, with some further tinkering on that code to just calculate the crossings you want (within a time range and in desired direction).
+-08-17 Updated Poincare-section GMRES-hookstep code for fixed points of Poincare map to higher accuracy intersections and general defns of sections. Have tested on coarse-discretized P19p02, gets f(u)-u==0 and I-D==0  to 1e-13.
+-08-17 Revised interpolation trajectories crossing Poincare section for higher accuracy. After quadratic interpolation of t that gives to f(u(t)) == 0, added a Newton search on t. This increases accuracy of interpolation from O(dt^3) to floating point. Though this accuracy is artificial, I think it will help remove spurious marginal eigenvalues in Arnoldi iteration of the Poincare map. I am going to compute the I==D poincare sections of all the HKW periodic orbits now.
+-08-14 PACE nodes are about 1/4 as fast as my new home home machine with a AMD Phenom II X4 955 CPU. It'll be faster to run at home and shut down the machine for sleep.
+-08-14 Generalized the Poincare-section code so that user can supply arbitrary f(u) to define section. Uses a functor class so that f can retain internal data for things like f(u) = (u - u*, e*) (internal data for f is u* and e*).  Am using this to compute intersection of HKW orbits with f(u) = I(u) - D(u) = 0. I think this will be a good section for partitioning and Markov model, since all orbits intersect this section.
+-08-13 Thankless professional activity.
+-08-10 Moved continuation calculations for localized solutions from home machine to PACE. Slept better last night without the computer humming.
+-08-04 Have refactored the adhoc Poincare-section / fundamental domain integration routines in such a way that they can be reused in different command-line routines. Imperfect but acceptable. Imperfect in that Poincare section is defined in a particular way, (u(t) - u*, e*) == 0, same for fundamental domain (u(t), e[n]) > 0, with symmetry sigma[n] mapping crossings back into fundamental domain via sigma[n] e[n] = -e[n]. Also imperfect in that function signatures are not identical to time-T integrations so swapping into Arnoldi and Newton_krylov code will require some tinkering. I am currently recomputing EQ2, its eigenfunctions, and P47 orbit in lower discretization (32 x 33 x 32) so that I can test this code with faster integrations.
+-08-04 Continuations of localized solutions continue running in background. Understanding how the localized EQB and TW bifurcate from the globally periodic EQB will take some thought and numerical effort. Thought is about expanding our Couette symmetry group classification to deal with quarter-shifts, eighth-shifts, etc., or better, to rephrase it in terms of finite shifts lx, lz in infinite domain. Numerical effort is to determine the symmetries/antisymmetries of the periodic EQB's eigenfunctions w.r.t the larger symmetry group and then
+center the EQBs and TWs already computed in proper phases so that they bifurcate from the same EQB, coordinated with the symmetries of the EQB eigenfunctions.
+-08-07 APS-DFD abstract submitted.
+-08-03 Finished paper review.
+-07-31 Sent off n00bs proofs.
+-07-30 Also figured out how to ''scp -pr'' from PACE to my home machine through an ssh tunnel on ssh.physics.gatech.edu, so I am copying my measly-but-overflowing 11 GB PACE account to my spacious home rig to make room for more PACE calculations. Watch out, pace-cns queue!
+-07-28 Found the typo that broke all traveling-wave searches so far in my career: The ''FieldSymmetry *= Real'' operator definition had ''ax_ = c*az_'' instead of ''az_ = c*az_'', where ''ax_, az_'' are finite translations and ''c'' is the multiplicative constant. When used in the Newton-Krylov-hookstep algorithm, this obliterated the small perturbations in finite-time shifts and made it impossible to converge onto solutions of the traveling-wave equations. Now am happily continuing localized traveling waves for 'even' half of odd/even snaking ladder.
+-07-30 Refactoring DNS algorithm advance functions to uniting end-on-section with end-at-time-T algorithms for unified findsoln, arnoldi, etc. is not so easy. At times like this I wish high-level channelflow were in Python. Might lower the goal and produce kludgier special-purpose command-line utils for poincare sections.
+-07-24 Significant progress yesterday and today on incorporating integration to Poincare sections into
+a DNS algorithm, so that section-to-section calculations is more self-contained and can be used within Arnoldi iteration, periodic orbit calculations, a command-line utility, etc. Today I figured out how to factor the previous command-line code into a DNS::advance function that works very similarly to the given-time-interval advance function. Have the code up and running and am testing it for proper behavior around EQ2.
+-07-23 Am working on the poincare sections. I believe I recently properly readjusted my understanding of what Predrag wants here and am revising my Poincare-section computing code to accomplish it. Namely, I'm adding moving what was previously a post-processing calculation into a DNS algorithm, so that simulations can be specified to end at a certain time or a certain geometric value (still using polynomial interpolation on u(t-2dt), u(t-dt), u(t) rather than replacing time with a space variable, which would require recalculating and refactoring implicit integration matrices at every step --difficult and inefficient). This will simplify the process of continuing and comparing the unstable manifolds of the equilibrium and the periodic orbit.
+-07-24 Respond to queries about forcing functions in channelflow howto blog.  Posted 2009-07-16.
+-07-22 Move channelflow SVN to channelflow.org. Will allow better access to source code for those outside Georgia Tech. Done right away because the svndump Roman made for me was getting stale. Posted 2007-07-20
+-07-18 Center the snaking-bifurcation solutions and compute their eigenspectra.
+-07-17 Write an ad-hoc program to translate localized solutions so they're s_xyz-symmetric about the center of the box. Took a whole day, longer than I thought.
+-07-16. Tobias is inclined to keep this to ourselves until publishing. I'll follow his lead since he let me in on the project.
 -06-11. PC: You might want to get in touch with [[http://www.mech.kth.se/~duguet/webpage.html|Yohann Duguet, KTH Stockholm]]. He has some interesting spatially localized equilibria for plane Couette.
@@ Line 38: / Line 121: @@
-===== computer upgrade =====
--06-09.
+-06-09. Computer upgrade
 I ended the semester with my PACE account (10 GB) and home computer (180 GB) crammed with thousands of binary flow fields
 from time integrations and parametric continuations. The time integrations can be recomputed pretty easily, but parametric

channelflow.org

User Tools

Site Tools

Page Tools