Many thanks, I think that is making more sense now. I assume I could also change D to be expressed in terms of 0.042**(2./3) to keep consistency? (It would be a bit of a bizarre setup I admit..)
As a separate question, if not boundary conditions are specified what does this default to? (If anything) On Wed, Apr 3, 2019 at 10:52 PM Guyer, Jonathan E. Dr. (Fed) via fipy < fipy@nist.gov> wrote: > Dario - > > 1) FiPy does have a mechanism for specifying units. See: > > > https://www.ctcms.nist.gov/fipy/fipy/generated/fipy.variables.html#fipy.variables.variable.Variable > > https://www.ctcms.nist.gov/fipy/fipy/generated/fipy.variables.html#fipy.variables.variable.Variable.inBaseUnits > > https://www.ctcms.nist.gov/fipy/fipy/generated/fipy.variables.html#fipy.variables.variable.Variable.inUnitsOf > > However, they don't propagate through the solvers, so you end up needing > to express your equations with dimensionless coefficients composed of > dimensional Variables. I'm not sure that anybody but me has ever tried to > use this feature, and I don't use it. > > I was not suggesting truly dimensional coefficients, though. Just pick a > self-consistent system, e.g., > > dx = dy = dz = .042**(1./3) # mm > dt = 15.125 # s > D = 0.001 # mm2/s > > FiPy doesn't care. You're going to pay the price for multiplying and > dividing everything by 1, anyway, so you might as well work with terms that > are easier to think about, at least for me. > > 2) I did not mean to suggest that the time step doesn't matter. Only that > the Fourier limit doesn't apply. > The Fourier limit is associated with *stability*. An explicit > discretization "blows up" if the Fourier limit is exceeded, but an implicit > discretization does not. Accuracy may suffer, however. > > This is all covered pretty methodically in examples/diffusion/mesh1D.py. > > > On Apr 3, 2019, at 4:35 PM, Dario Panada <dario.pan...@gmail.com> wrote: > > > > Hi Jonathan, > > > > Many thanks for your quick response. > > > > Firstly apologies if I'm asking rather basic questions, I'm still new to > FiPy and learning. I've read the manual but if you think there are any > sections I would benefit from re-reading, or any additional resources, > please feel free to point me to them as an answer. > > > > 1) So how do I specify/enforce units? For example, I'm setting my > diffusivity in mm2/s. I could convert this to cm2/s and put that obviously > different value for D. How does FiPy know I've changed the units? Or should > I make my units consistent with the spatial discretization? (Ie: If I use > mm3 then my diffusivity should use mm2.) But then how about the time unit? > What if I converted from mm2/s to mm2/hour? > > > > 2) In my case, changing dt does affect the final output all other things > being equal. (However, I am using integer for dx etc. Maybe that's why?) > > > > Kind Regards, > > Dario > > > > On Wed, Apr 3, 2019 at 8:48 PM Guyer, Jonathan E. Dr. (Fed) via fipy < > fipy@nist.gov> wrote: > > Dario - > > > > - FiPy's DiffusionTerm is implicit, so there is no Fourier limit on your > time step. > > > > - There's no particular advantage to scaling length and time to 1 > > > > - Be sure to set dx = dy = dz = 1., a float, not dx = dy = dz = 1, an > integer > > > > - Jon > > > > > On Apr 3, 2019, at 11:28 AM, Dario Panada <dario.pan...@gmail.com> > wrote: > > > > > > Hello, > > > > > > I am trying to use FiPy to build a system to simulate oxygen diffusion > in tissues in 3D. > > > > > > My grid is a 20x20x20 mesh, defined as: > > > > > > mesh=Grid3D(dx=dx,dy=dy,nx=nx,ny=ny, dz=dz, nz=nz) > > > > > > Where nx = ny = nz = 20 and dx = dy = dz = 1. This approach is taken > from examples.diffusion.mesh1D, where nx was set to 50 and dx to 1 to > represent unity. > > > > > > I setup my equation as: > > > > > > eq=TransientTerm()==DiffusionTerm(coeff=D) + sourceGrid - sinkGrid > > > > > > My oxygen diffusion coefficient (D) is 0.001 mm2/s. Each cell is my > grid corresponds to 0.042 mm3. So (Δx)^3 = 0.042mm^3 which implies (Δx^2) > ~=0.121 mm2. > > > > > > I understand that for 3D problems the Fourier number (Fo) has to be > less than or equal to 1/8. > > > > > > With Fo = DΔt/(Δx^2) <= 1/8 so Δt <= (Δx^2)/(8D) where replacing > values I get Δt <= 15.125 . > > > > > > From the above, would it be sensible to setup my script as? > > > --- > > > nx = ny = nz = 20 > > > dx = dy = dz = 1 > > > dt = 1 > > > D = 0.121 > > > mesh=Grid3D(dx=dx,dy=dy,nx=nx,ny=ny, dz=dz, nz=nz) > > > > > > phi=CellVariable(name="solutionvariable",mesh=mesh,value=0.) > > > > > > eq=TransientTerm()==DiffusionTerm(coeff=D) + sourceGrid - sinkGrid > > > > > > eq.solve(var=phi,dt=dt) > > > --- > > > > > > Or am I missing something/have interpreted something wrong? > > > > > > Kind Regards, > > > Dario > > > _______________________________________________ > > > 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 ] >
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