Fabien - I don't know where the problem lies, but my recommendation would be to systematically take the problem back toward the code I previously gave you. While that code didn't produce the image you were looking for, the behavior seemed consistent and it wasn't unstable.

As far as I can tell, in addition to changing the initial condition and the boundary conditions, you've increased the Peclét number by three orders of magnitude (by including c in DT) and increased the thermal dilatation by factor of 10 (by changing to a temperature delta from a dimensionless value +/- 1 to an absolute temperature difference). By changing these parameters back, you may regain the earlier stability and get some insight as to what the problem is. - Jon > On Sep 18, 2018, at 3:10 AM, fgendr01 <fabien.gend...@univ-lr.fr> wrote: > > Yes I tried without kinematic boundary conditions and there is no difference ! > Maybe the scheme is not stable. > Other ideas ? > > Fabien > >> Le 17 sept. 2018 à 22:27, Thibault Bridel-Bertomeu >> <thibault.bridellel...@gmail.com> a écrit : >> >> Have you tried without the kinematic boundary conditions ? Just constrain T >> and dT/dn, what happens then ? >> >> Le lun. 17 sept. 2018 à 22:17, fgendr01 <fabien.gend...@univ-lr.fr> a écrit : >> Alas, it doesn’t work :-( >> I tried to change the CFL condition but there is not real differences… >> 2 screenshots at t = 0 and after 20s... >> >> <PastedGraphic-5.png> >> >> If someone have the solution ? >> >> here is the code with last modifications : >> >> # -*- coding: utf-8 -*- >> from fipy import * >> import matplotlib.pyplot as plt >> # Parameter >> L = 1. >> N = 100. >> dL = L/N >> T0 = 293. >> Tmax = 303. # Temperature max >> Tmin = 283. # Temperature min >> alpha = 0.0002 # Thermal dilatation >> lamda = 0.6 # Thermal conductivity (W/m/K) >> c = 4186. # Specific Heat of sea >> water (J/kg/K) >> ro0 = 1023. # average density of sea water >> g = 10. # Gravity (m/s2) >> DT = lamda/(c*ro0) # Thermal diffusivity (m2/s) >> # Mesh >> mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) >> # Variables >> T = CellVariable(mesh=mesh, name = 'T', value = T0) >> xVelocity = CellVariable(mesh=mesh, name='Xvelocity', value = 0.) >> zVelocity = CellVariable(mesh=mesh, name='Zvelocity', value = 0.) >> velocity = FaceVariable(mesh=mesh, name='velocity', rank=1) >> # Init Condition >> T.setValue(T0) >> # Boundary Conditions >> T.constrain(Tmax, mesh.facesLeft) #Tmax to the >> Left >> T.constrain(Tmin, mesh.facesRight) #Tmin to the right >> T.faceGrad.constrain(0, mesh.facesTop) #Adiabatic wall to the >> Top >> T.faceGrad.constrain(0, mesh.facesBottom) #Adiabatic wall to the >> Bottom >> xVelocity.constrain(0, mesh.facesLeft) >> xVelocity.constrain(0, mesh.facesRight) >> zVelocity.constrain(0, mesh.facesTop) >> zVelocity.constrain(0, mesh.facesBottom) >> # Viewer >> viewer = None >> if __name__ == '__main__': >> viewer = Viewer(vars=T, datamin=Tmin, datamax=Tmax) >> viewer.plot() >> raw_input("<Enter to continue>...") >> # Boussinesq equations >> eqX = (TransientTerm(var=xVelocity) + ConvectionTerm (var=xVelocity, >> coeff=velocity) == 0) >> eqZ = (TransientTerm(var=zVelocity) + ConvectionTerm (var=zVelocity, >> coeff=velocity) == alpha*g*(T-T0)) >> eqT = (TransientTerm(var=T) + ConvectionTerm (var=T, coeff=velocity) == >> DiffusionTerm(var=T, coeff=DT)) >> eq = eqX & eqZ & eqT >> # Solving Boussinesq equations >> timeStepDuration = 0.001*dL**2/(2*DT) #CFL Condition >> steps = 50 >> sweeps = 5 >> for step in range(steps): >> for sweep in range(sweeps): >> eq.sweep(dt=timeStepDuration) >> velocity[0] = xVelocity.arithmeticFaceValue >> velocity[1] = zVelocity.arithmeticFaceValue >> velocity[..., mesh.exteriorFaces.value] = 0. >> if viewer is not None: >> viewer.plot() >> plt.pause(0.1) >> raw_input("<Enter to finish>… ") >> >> >> Sorry for all my messages... >> >> Fabien >> >> >>> Le 17 sept. 2018 à 21:52, Thibault Bridel-Bertomeu >>> <thibault.bridellel...@gmail.com> a écrit : >>> >>> Hi again Fabien, >>> >>> Well, I would say that physically it makes sense. With such boundary >>> condition, I think the problem is well posed. Now it is all about the >>> numerics. >>> Have you tried ? What does the solver yield ? >>> >>> Cheers >>> Thibault >>> Le lun. 17 sept. 2018 à 21:49, fgendr01 <fabien.gend...@univ-lr.fr> a écrit >>> : >>> Thanks Thibault, >>> You’re right, the top ans the bottom walls are adiabatic and I tried to put >>> velocity conditions. >>> What do you think about these conditions : >>> >>> # Boundary Conditions >>> T.constrain(Tmax, mesh.facesLeft) >>> T.constrain(Tmin, mesh.facesRight) >>> T.faceGrad.constrain(0, mesh.facesTop) >>> T.faceGrad.constrain(0, mesh.facesBottom) >>> xVelocity.constrain(0, mesh.facesLeft) >>> xVelocity.constrain(0, mesh.facesRight) >>> zVelocity.constrain(0, mesh.facesTop) >>> zVelocity.constrain(0, mesh.facesBottom) >>> >>> Thanks, >>> >>> Fabien >>> >>>> Le 17 sept. 2018 à 21:29, Thibault Bridel-Bertomeu >>>> <thibault.bridellel...@gmail.com> a écrit : >>>> >>>> Good evening Fabien, >>>> >>>> I have not been following the development or the answers given to you by >>>> other members, so, apologies if I stumble on something that’s already been >>>> told. >>>> >>>> I think the figure you send with your question is the answer. From what I >>>> can see, at the top and the bottom of the domain, there is some >>>> extrapolation going on, or Neumann sort of boundary condition : the >>>> temperature gradient is zero. In physical terms, those two walls look >>>> adiabatic to me. >>>> >>>> I don’t have my laptop anywhere close but I would encourage you to browse >>>> the examples to find an adiabatic or zero-gradient boundary condition ! >>>> >>>> As for the mathematical aspect of your question: when it comes to the >>>> Navier-Stokes equations, you have to impose boundary conditions on all >>>> boundary patches of the domain. The boundary conditions can change >>>> depending on what you want to happen, but you have to have one. Also it is >>>> surprising to me that only imposing the temperature on the left and right >>>> patches is enough: I’m not sure about fipy core behavior, but with >>>> Navier-Stokes, you gotta impose temperature and velocity to have a >>>> well-posed problem ! >>>> >>>> Cheers and bon courage ! >>>> >>>> T >>>> Le lun. 17 sept. 2018 à 21:09, fgendr01 <fabien.gend...@univ-lr.fr> a >>>> écrit : >>>> Hi Jon and the community, >>>> >>>> Since a few weeks, I develop a small code to solve a 2D problem of water >>>> transport in a simple mesh. >>>> My problem is the resolution of the Navier-Stokes equations with the >>>> Boussinesq approximation in 2D with a thermal gradient. >>>> I try to solve these equations : >>>> >>>> A member (Jonathan) helped me and wrote a part of the code but the code >>>> seems not to be stable and I don’t know why ! >>>> Can you help me ? >>>> There must be a problem with the boundary conditions. >>>> I want to impose a fixed temperature on the left wall (303K) and a fixed >>>> temperature on the right wall (283K). Should I put a condition on the >>>> upper and lower walls? >>>> Here is my code : >>>> >>>> # -*- coding: utf-8 -*- >>>> from fipy import * >>>> import matplotlib.pyplot as plt >>>> # Parameter >>>> L = 1. >>>> N = 100. >>>> dL = L/N >>>> T0 = 293. >>>> Tmax = 303. # Temperature max >>>> Tmin = 283. # Temperature min >>>> alpha = 0.0002 # Thermal dilatation >>>> lamda = 0.6 # Thermal conductivity >>>> (W/m/K) >>>> c = 4186. # Specific Heat of sea >>>> water (J/kg/K) >>>> ro0 = 1023. # average density of >>>> sea water >>>> g = 10. # Gravity (m/s2) >>>> DT = lamda/(c*ro0) # Thermal diffusivity (m2/s) >>>> # Mesh >>>> mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) >>>> # Variables >>>> T = CellVariable(mesh=mesh, name = 'T', value = T0) >>>> xVelocity = CellVariable(mesh=mesh, name='Xvelocity', value = 0.) >>>> zVelocity = CellVariable(mesh=mesh, name='Zvelocity', value = 0.) >>>> velocity = FaceVariable(mesh=mesh, name='velocity', rank=1) >>>> # Init Condition >>>> T.setValue(T0) >>>> # Boundary Conditions >>>> T.constrain(Tmax, mesh.facesLeft) >>>> T.constrain(Tmin, mesh.facesRight) >>>> # Viewer init conditions >>>> viewer = None >>>> if __name__ == '__main__': >>>> viewer = Viewer(vars=T, datamin=Tmin, datamax=Tmax) >>>> viewer.plot() >>>> raw_input("<Enter to continue>...") >>>> # Boussinesq equations >>>> eqX = (TransientTerm(var=xVelocity) + ConvectionTerm (var=xVelocity, >>>> coeff=velocity) == 0) >>>> eqZ = (TransientTerm(var=zVelocity) + ConvectionTerm (var=zVelocity, >>>> coeff=velocity) == alpha*g*(T-T0)) >>>> eqT = (TransientTerm(var=T) + ConvectionTerm (var=T, coeff=velocity) == >>>> DiffusionTerm(var=T, coeff=DT)) >>>> eq = eqX & eqZ & eqT >>>> # Solving Boussinesq equations >>>> timeStepDuration = 0.1*dL**2/(2*DT) >>>> steps = 50 >>>> sweeps = 5 >>>> for step in range(steps): >>>> for sweep in range(sweeps): >>>> eq.sweep(dt=timeStepDuration) >>>> velocity[0] = xVelocity.arithmeticFaceValue >>>> velocity[1] = zVelocity.arithmeticFaceValue >>>> velocity[..., mesh.exteriorFaces.value] = 0. >>>> if viewer is not None: >>>> viewer.plot() >>>> plt.pause(0.1) >>>> raw_input("<Enter to finish>… ") >>>> >>>> I’d like to obtain something like this : >>>> >>>> >>>> Thanks again for your help, maybe Jon again ;-) >>>> >>>> Fabien >>>> >>>> >>>>> Le 16 août 2018 à 07:20, fgendr01 <fabien.gend...@univ-lr.fr> a écrit : >>>>> >>>>> Thanks a lot Jon. >>>>> I appreciate your help. >>>>> I will try to apply your remarks but I will certainly still need your >>>>> help again ;-) to develop the code. >>>>> >>>>> Thanks again. >>>>> >>>>> Fabien >>>>> >>>>>> Le 15 août 2018 à 19:46, Guyer, Jonathan E. Dr. (Fed) >>>>>> <jonathan.gu...@nist.gov> a écrit : >>>>>> >>>>>> Fabien - >>>>>> >>>>>> I think the code below should get you going. >>>>>> >>>>>> The changes I made were: >>>>>> >>>>>> - `xVelocity` and `zVelocity` changed to rank-0 CellVariables. FiPy >>>>>> *always* solves at cell centers. >>>>>> - Created a rank-1 FaceVariable to hold the velocity. The cell >>>>>> components must be interpolated and manually inserted into this field at >>>>>> each sweep. >>>>>> - Changed the sign of the DiffusionTerm in the heat equation; it's >>>>>> unconditionally unstable otherwise >>>>>> - Slowed down the time steps to better see the evolution >>>>>> >>>>>> The result is not identical to the image you showed, but I think that's >>>>>> down to boundary conditions, sign of gravity, etc. >>>>>> >>>>>> - Jon >>>>>> >>>>>> # -*- coding: utf-8 -*- >>>>>> from fipy import * >>>>>> import matplotlib.pyplot as plt >>>>>> # Parameter >>>>>> L = 1. >>>>>> N = 50. >>>>>> dL = L/N >>>>>> alpha = 0.0002 # Thermical dilatation >>>>>> landa = 0.6 # Thermical conductivity >>>>>> ro0 = 1023. # Average volumic Mass >>>>>> g = 10. # Gravity >>>>>> # Mesh >>>>>> mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) >>>>>> # Variables >>>>>> dT = CellVariable(name = 'dT', mesh = mesh, value = 0.) >>>>>> xVelocity = CellVariable(mesh=mesh, name='Xvelocity', value = 0.) >>>>>> zVelocity = CellVariable(mesh=mesh, name='Zvelocity', value = 0.) >>>>>> velocity = FaceVariable(mesh=mesh, name='velocity', rank=1) >>>>>> # Init Condition >>>>>> x = mesh.cellCenters[0] >>>>>> dT.setValue(1.) >>>>>> dT.setValue(-1., where = x > L/2) >>>>>> # Viewer >>>>>> viewer = None >>>>>> if __name__ == '__main__': >>>>>> viewer = Viewer(vars=dT, datamin=-1., datamax=1.) >>>>>> viewer.plotMesh() >>>>>> raw_input("<Enter to continue>...") >>>>>> # Boussinesq equations >>>>>> D = landa/ro0 >>>>>> eqX = (TransientTerm(var=xVelocity) + ConvectionTerm (var=xVelocity, >>>>>> coeff=velocity) == 0) >>>>>> eqZ = (TransientTerm(var=zVelocity) + ConvectionTerm (var=zVelocity, >>>>>> coeff=velocity) + alpha*g*dT == 0) >>>>>> eqT = (TransientTerm(var=dT) + ConvectionTerm (var=dT, coeff=velocity) >>>>>> == DiffusionTerm(var=dT, coeff=D)) >>>>>> eq = eqX & eqZ & eqT >>>>>> # Solving Boussinesq equations >>>>>> timeStepDuration = 1 * dL**2 / (2 * D) >>>>>> steps = 50 >>>>>> sweeps = 5 >>>>>> for step in range(steps): >>>>>> for sweep in range(sweeps): >>>>>> eq.sweep(dt=timeStepDuration) >>>>>> velocity[0] = xVelocity.arithmeticFaceValue >>>>>> velocity[1] = zVelocity.arithmeticFaceValue >>>>>> velocity[..., mesh.exteriorFaces.value] = 0. >>>>>> if viewer is not None: >>>>>> viewer.plot() >>>>>> plt.pause(0.1) >>>>>> raw_input("<Enter to finsh>… ") >>>>>> >>>>>> >>>>>>> On Aug 14, 2018, at 11:22 AM, fgendr01 <fabien.gend...@univ-lr.fr> >>>>>>> wrote: >>>>>>> >>>>>>> Hello, >>>>>>> >>>>>>> I’m a PhD Student in La Rochelle University (France) and I’m working on >>>>>>> Boussinesq Approximation. >>>>>>> I’m starting with fipy and I’d like to make a little algorithm to solve >>>>>>> these equations in 2D (x,z) : >>>>>>> <PastedGraphic-1.png> >>>>>>> In my problem T = T0 + dT. >>>>>>> (ux, uz) is the velocity. >>>>>>> >>>>>>> So, here is my algorithm : >>>>>>> # -*- coding: utf-8 -*- >>>>>>> from fipy import * >>>>>>> import matplotlib.pyplot as plt >>>>>>> # Parameter >>>>>>> L = 1. >>>>>>> N = 50. >>>>>>> dL = L/N >>>>>>> alpha = 0.0002 # Thermical dilatation >>>>>>> landa = 0.6 # Thermical conductivity >>>>>>> ro0 = 1023. # Average volumic Mass >>>>>>> g = 10. # Gravity >>>>>>> # Mesh >>>>>>> mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) >>>>>>> # Variables >>>>>>> dT = CellVariable(name = 'dT', mesh = mesh, value = 0.) >>>>>>> xVelocity = FaceVariable(mesh=mesh, name='Xvelocity', value = 0., >>>>>>> rank=1) >>>>>>> zVelocity = FaceVariable(mesh=mesh, name='Zvelocity', value = 0., >>>>>>> rank=1) >>>>>>> # Init Condition >>>>>>> x = mesh.cellCenters[0] >>>>>>> dT.setValue(1.) >>>>>>> dT.setValue(-1., where = x > L/2) >>>>>>> # Viewer >>>>>>> viewer = None >>>>>>> if __name__ == '__main__': >>>>>>> viewer = Viewer(vars=dT, datamin=-1., datamax=1.) >>>>>>> viewer.plotMesh() >>>>>>> raw_input("<Enter to continue>...") >>>>>>> # Boussinesq equations >>>>>>> D = landa/ro0 >>>>>>> velocity = ((xVelocity), (zVelocity)) >>>>>>> eqX = (TransientTerm(var=xVelocity) + ConvectionTerm (var=xVelocity, >>>>>>> coeff=velocity) == 0) >>>>>>> eqZ = (TransientTerm(var=zVelocity) + ConvectionTerm (var=zVelocity, >>>>>>> coeff=velocity) + alpha*g*dT == 0) >>>>>>> eqT = (TransientTerm(var=dT) + ConvectionTerm (var=dT, coeff=velocity) >>>>>>> == -DiffusionTerm(var=dT, coeff=D)) >>>>>>> eq = eqX & eqZ & eqT >>>>>>> # Solving Boussinesq equations >>>>>>> timeStepDuration = 10 * dL**2 / (2 * D) >>>>>>> steps = 50 >>>>>>> for step in range(steps): >>>>>>> eq.solve(dt=timeStepDuration) >>>>>>> if viewer is not None: >>>>>>> viewer.plot() >>>>>>> plt.pause(0.1) >>>>>>> raw_input("<Enter to finsh>… ») >>>>>>> >>>>>>> My error : all the input arrays must have same number of dimensions >>>>>>> >>>>>>> I’d like to obtain something like this : >>>>>>> <PastedGraphic-3.png> >>>>>>> >>>>>>> If someone can help me, I will be very happy. >>>>>>> >>>>>>> Thanks a lot. >>>>>>> >>>>>>> Fabien G. >>>>>>> _______________________________________________ >>>>>>> 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 ] >>>> <PastedGraphic-2.png><PastedGraphic-1.png><PastedGraphic-2.png>_______________________________________________ >>>> >>>> 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 ] > > _______________________________________________ > 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 ]