In (intentionally) provocative terms, PDEs with analytical solutions aren't good for anything.
If I want to develop a qualitative understanding of the neutron flux and temperature in a nuclear reactor, I can make considerable headway with Bessel functions in cylindrically symmetric coordinates and a piece of paper. If I want to understand in detail which coolant channels and where in a real reactor are most likely to develop boiling conditions that choke off flow and cause neighboring fuel elements to melt, then I need a numerical simulation of a coupled set of PDEs governing neutron generation and absorption, multi-phase fluid flow, heat transport and generation, phase transformation of fuel, matrix, and cladding materials, and so on and so on. More simplistically, our first example demonstrates several cases of diffusion in 1D for basic reason that there are analytical solutions to validate against and many people have seen them before. Increase the number of dimensions, alter the boundary conditions, or introduce nonlinear coefficients, and there no longer are analytical solutions. If mathematical analysis of PDEs is your goal, FiPy probably isn't the tool for you. > On May 23, 2017, at 1:08 PM, Sergio Manzetti <sergio.manze...@fjordforsk.no> > wrote: > > Yes, just the first. But I am still not familiar with the point of numerical > simulations, I have bought a book on it, and read a few papers, but they all > don't explain the core intention of numerical sims: > > If it is not to solve the PDE, what is the point of inserting a > trial-function unless it has some analytical validity (thus analytical method > is required anyway), and therefore what is the real gain of getting a plot of > a numerical representation of the change of the solution during a given time > frame? > > If there was an example as simple as "one box of apples of 24 apples times > two makes 48 apples" to illustrate what we can get out of a numerical sim, > that would be excellent. But also that is difficult to find, even on google. > > Thanks! > Sergio > > Sergio Manzetti > > > > Fjordforsk AS > Midtun > 6894 Vangsnes > Norge > Org.nr. 911 659 654 > Tlf: +47 57695621 > Økolab | Nanofactory | AQ-Lab | FAP > > > From: "jonathan guyer" <jonathan.gu...@nist.gov> > To: "fipy" <FIPY@nist.gov> > Sent: Tuesday, May 23, 2017 5:04:59 PM > Subject: Re: Complex conjugates in FiPY > > Have you worked through the examples on our website and in our manual? > > > On May 23, 2017, at 9:58 AM, Sergio Manzetti > > <sergio.manze...@fjordforsk.no> wrote: > > > > Dear Jonathan. Thank your for this clarification. Can you recommend me a > > tutorial or a paper of numerical simuation which shows the use of the > > numerical output (plots or other data)? > > > > Thanks > > > > Sergio > > > > > > Sergio Manzetti > > > > > > > > Fjordforsk AS > > Midtun > > 6894 Vangsnes > > Norge > > Org.nr. 911 659 654 > > Tlf: +47 57695621 > > Økolab | Nanofactory | AQ-Lab | FAP > > > > > > From: "jonathan guyer" <jonathan.gu...@nist.gov> > > To: "fipy" <FIPY@nist.gov> > > Sent: Tuesday, May 23, 2017 3:34:51 PM > > Subject: Re: Complex conjugates in FiPY > > > > > On May 23, 2017, at 8:05 AM, Sergio Manzetti > > > <sergio.manze...@fjordforsk.no> wrote: > > > > > > I am not sure what the script does, when one sets a phi value before the > > > given PDE...when I thought that the phi value was found exactly by FipY? > > > > Setting phi before solving the PDE is setting the initial condition. FiPy > > is designed to ***numerically*** solve time-evolving PDEs. > > > > > > _______________________________________________ > > fipy mailing list > > fipy@nist.gov > > http://www.ctcms.nist.gov/fipy > > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > _______________________________________________ > > fipy mailing list > > fipy@nist.gov > > http://www.ctcms.nist.gov/fipy > > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
