Re: Solving convection only problem
Thanks for the reply. I searched more and just realized this question has been answered before. I then switched to VanLeerConvectionTerm, It turns out this method is able to keep the shock pretty well which has been mentioned in the previous posts. I might try CLAWPACK in the future, but I think the VanLeer terms is good for my project for now. Thanks again. Best, Zhekai On Thu, Oct 20, 2016 at 9:05 AM, Daniel Wheeler wrote: > Hi Zhekai, > > There is generally a lot of numerical diffusion when solving > convection problems with first order schemes and even some numerical > diffusion when using higher order schemes. There are many different > schemes and a mass of literature on how to preserve square waves, > shocks and hyperbolic equations, but FiPy doesn't have any of those > schemes implemented (e.g. TVD schemes come to mind). There is also a > secondary issue when coupling hyperbolic equations to do with how the > flux is calculated that FiPy doesn't address (the Riemann problem, roe > solvers etc). However, for many convection-diffusion problems the time > scale of the shocks is not worth resolving or is impossible to resolve > while also resolving much longer time scales. When resolving at the > convection time scale there is often no benefit from the implicit > schemes that FiPy uses. Basically, FiPy is not a great tool for shock > problems. CLAWPACK may be something that you could look at for this. I > think it's fully explicit and it's focus is on hyperbolic coupled > equations. > > I hope that helps. > > Cheers, > > Daniel > > On Thu, Oct 20, 2016 at 12:58 AM, Zhekai Deng > wrote: > > Hi all, > > > > I am trying to use Fipy to solve convection only problem for the > > concentration moved only by solid body rotation in a "circular" shape > > geometry. > > > > By looking at the examples online, I found out that > > > > http://www.ctcms.nist.gov/fipy/examples/convection/ > generated/examples.convection.source.html#module-examples. > convection.source > > > > and some of the level set example appears to allow me do it. > > > > I implemented the approach from convection example. However, the solution > > still looks has diffusion ( or maybe artificial smoothness ) as the > > concentration move with velocity field. I have attached my example code, > > that concentration enter from the top right side of the geometry, and > > undergo solid body rotation eventually to the left side, and flow out of > the > > domain. So my question is that is there any way to further reduce the > > diffusion? Also, does anyone know where this "diffusion" is coming from ? > > > > The approach that I have tried but did not work are following: > > 1. Solve the equation with very small diffusion coefficient (1e-8) > > 2. Reduce the timestep or refine the mesh size does not seem to help very > > much > > > > I have attached my example code in this email. Thank you very much. > > > > Best, > > > > Zhekai > > > > > > ___ > > fipy mailing list > > fipy@nist.gov > > http://www.ctcms.nist.gov/fipy > > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > > > > > -- > Daniel Wheeler > ___ > 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 ]
Re: Solving convection only problem
Hi Zhekai, There is generally a lot of numerical diffusion when solving convection problems with first order schemes and even some numerical diffusion when using higher order schemes. There are many different schemes and a mass of literature on how to preserve square waves, shocks and hyperbolic equations, but FiPy doesn't have any of those schemes implemented (e.g. TVD schemes come to mind). There is also a secondary issue when coupling hyperbolic equations to do with how the flux is calculated that FiPy doesn't address (the Riemann problem, roe solvers etc). However, for many convection-diffusion problems the time scale of the shocks is not worth resolving or is impossible to resolve while also resolving much longer time scales. When resolving at the convection time scale there is often no benefit from the implicit schemes that FiPy uses. Basically, FiPy is not a great tool for shock problems. CLAWPACK may be something that you could look at for this. I think it's fully explicit and it's focus is on hyperbolic coupled equations. I hope that helps. Cheers, Daniel On Thu, Oct 20, 2016 at 12:58 AM, Zhekai Deng wrote: > Hi all, > > I am trying to use Fipy to solve convection only problem for the > concentration moved only by solid body rotation in a "circular" shape > geometry. > > By looking at the examples online, I found out that > > http://www.ctcms.nist.gov/fipy/examples/convection/generated/examples.convection.source.html#module-examples.convection.source > > and some of the level set example appears to allow me do it. > > I implemented the approach from convection example. However, the solution > still looks has diffusion ( or maybe artificial smoothness ) as the > concentration move with velocity field. I have attached my example code, > that concentration enter from the top right side of the geometry, and > undergo solid body rotation eventually to the left side, and flow out of the > domain. So my question is that is there any way to further reduce the > diffusion? Also, does anyone know where this "diffusion" is coming from ? > > The approach that I have tried but did not work are following: > 1. Solve the equation with very small diffusion coefficient (1e-8) > 2. Reduce the timestep or refine the mesh size does not seem to help very > much > > I have attached my example code in this email. Thank you very much. > > Best, > > Zhekai > > > ___ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > -- Daniel Wheeler ___ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
Solving convection only problem
Hi all,
I am trying to use Fipy to solve convection only problem for the
concentration moved only by solid body rotation in a "circular" shape
geometry.
By looking at the examples online, I found out that
http://www.ctcms.nist.gov/fipy/examples/convection/
generated/examples.convection.source.html#module-examples.convection.source
and some of the level set example appears to allow me do it.
I implemented the approach from convection example. However, the solution
still looks has diffusion ( or maybe artificial smoothness ) as the
concentration move with velocity field. I have attached my example code,
that concentration enter from the top right side of the geometry, and
undergo solid body rotation eventually to the left side, and flow out of
the domain. So my question is that is there any way to further reduce the
diffusion? Also, does anyone know where this "diffusion" is coming from ?
The approach that I have tried but did not work are following:
1. Solve the equation with very small diffusion coefficient (1e-8)
2. Reduce the timestep or refine the mesh size does not seem to help very
much
I have attached my example code in this email. Thank you very much.
Best,
Zhekai
from fipy import *
import numpy as np
import matplotlib as matplotlib_plot
mesh_2 = Gmsh2D('''
lc = 1e-2;
Point(1) = {-1, 0, 0, lc};
Point(2) = {0, 0, 0, lc};
Point(3) = {1, 0, 0, lc};
Point(4) = {0,-0.1,0,lc};
Ellipse(5) = {1,2,2,4};
Ellipse(6) = {4,2,2,3};
Line(7) = {3,2};
Line(8) = {2,1};
Circle(9) = {1,2,3};
Line Loop(9) = {6,7, 8,5};
Line Loop(10) = {-6,-5,9};
Plane Surface (12) = {10};
Physical Surface("bulk_flow") = {12};
Physical Line("Bottom_Left") = {5};
Physical Line("Bottom_Right") = {6};
''' % locals())
phi_2 = CellVariable(name = "solution variable",
mesh = mesh_2,
value = 0.) # doctest: +GMSH
xFace_2,yFace_2=mesh_2.faceCenters
velocityX_2 = yFace_2
velocityY_2 = -xFace_2
velocityVector_2 = FaceVariable(mesh=mesh_2, rank=1)
velocityVector_2[0] = velocityX_2
velocityVector_2[1] = velocityY_2
exit_velocityX_2 = yFace_2
exit_velocityY_2 = -xFace_2
exit_velocityVector_2 = FaceVariable(mesh=mesh_2, rank=1)
exit_velocityVector_2[0] = exit_velocityX_2
exit_velocityVector_2[1] = exit_velocityY_2
out_flow_mask_2 = ((xFace_2 <= 0.) & (yFace_2 < 0.))
exteriorCoeff_2 = FaceVariable(mesh_2, value=exit_velocityVector_2, rank=1)
exteriorCoeff_2.setValue([[0.],[0.]], where= ~(mesh_2.exteriorFaces &
mesh_2.physicalFaces["Bottom_Left"]))
velocityVector_2.setValue([[0.],[0.]], where= mesh_2.exteriorFaces &
mesh_2.physicalFaces["Bottom_Left"])
eq = TransientTerm() \
+ PowerLawConvectionTerm(coeff = velocityVector_2)\
+ ImplicitSourceTerm(exteriorCoeff_2.divergence) == 0
phi_2.constrain(1., where = mesh_2.exteriorFaces &
mesh_2.physicalFaces["Bottom_Right"]) # doctest: +GMSH
viewer_2 = Matplotlib2DViewer(vars=phi_2, title="final solution", cmap =
matplotlib_plot.cm.hot,datamin = 0., datamax = 1.)
timeStepDuration = 1/200.
steps = 800
for step in range(steps):
eq.sweep(var=phi_2,dt=timeStepDuration) # doctest: +GMSH
viewer_2.plot()___
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