Thanks for you help so far. I will be more explicit in what I am doing. The
equations are:
[image: \frac{\partial}{\partial t}\left(n\right)+\frac{\partial}{\partial
x}\left(nv\right)=S_n]
[image: \frac{\partial}{\partial t}\left(m_i n
v\right)+\frac{\partial}{\partial x}\left(m_i
nv^2\right)=S_m-\frac{\partial}{\partial x}\left(nT_e+nT_i\right)]
[image: \frac{\partial}{\partial
t}\left(\frac{3}{2}nT_e\right)+\frac{\partial}{\partial
x}\left(\frac{5}{2}nvT_e\right)=S_{q,e}]
[image: \frac{\partial}{\partial t}\left(\frac{3}{2}nT_i+\frac{1}{2}m_i
nv^2\right)+\frac{\partial}{\partial
x}\left(\frac{5}{2}nvT_i+\frac{1}{2}m_i nv^3\right)=S_{q,i}]
With n, v, Te, and Ti the variables, x the spatial dimension, t the
temporal dimension, and m a constant. The S-terms are source terms, which
will get more complicated as I progress (including a thermal conductivity
with a T-dependent coefficient). To solve, for now ignoring the terms with
m in the last equation for simplicity, I have tried recasting them in the
form:
[image: \frac{\partial}{\partial
t}\left(f_0\right)+\frac{\partial}{\partial
x}\left(\frac{1}{m}f_1\right)=S_0]
[image: \frac{\partial}{\partial
t}\left(f_1\right)+\frac{\partial}{\partial
x}\left(\frac{1}{m}\frac{f_1^2}{f_0}\right)=S_1-\frac{\partial}{\partial
x}\left(\frac{2}{3}f_2+\frac{2}{3}f_3\right)]
[image: \frac{\partial}{\partial
t}\left(f_2\right)+\frac{\partial}{\partial x}\left(\frac{3}{5m}\frac{f_1
f_2}{f_0}\right)=S_{2}]
[image: \frac{\partial}{\partial
t}\left(f_3\right)+\frac{\partial}{\partial x}\left(\frac{3}{5m}\frac{f_1
f_3}{f_0}\right)=S_{3}]
I roughly follow the process laid out in the coupled diffusion equations
example:
from fipy import *
mesh = Grid1D(nx = 100, Lx = 1.0)
m = 1.0
f0 = CellVariable(mesh = mesh, hasOld = True, value = 0.5, name = 'f0')
f1 = CellVariable(mesh = mesh, hasOld = True, value = 0.5, name = 'f1')
f2 = CellVariable(mesh = mesh, hasOld = True, value = 0.5, name = 'f2')
f3 = CellVariable(mesh = mesh, hasOld = True, value = 0.5, name = 'f3')
f0.constrain(0, mesh.facesLeft)
f0.constrain(1, mesh.facesRight)
f1.constrain(0, mesh.facesLeft)
f1.constrain(1, mesh.facesRight)
f2.constrain(0, mesh.facesLeft)
f2.constrain(1, mesh.facesRight)
f3.constrain(0, mesh.facesLeft)
f3.constrain(1, mesh.facesRight)
s0 = 0.0
s1 = 0.0
s2 = 0.0
s3 = 0.0
eq0 = TransientTerm(var = f0) + ExponentialConvectionTerm(coeff = (1.0/m,),
var = f1) == s0
eq1 = TransientTerm(var = f1) + ExponentialConvectionTerm(coeff = (1.0/m,),
var = f1**2/f0) == s1 - ExponentialConvectionTerm(coeff = (2/3.0,), var =
f2) - ExponentialConvectionTerm(coeff = (2/3.0,), var = f3)
eq2 = TransientTerm(var = f2) + ExponentialConvectionTerm(coeff =
(3.0/(5*m),), var = f1*f2/f0) == s2
eq3 = TransientTerm(var = f3) + ExponentialConvectionTerm(coeff =
(3.0/(5*m),), var = f1*f3/f0) == s3
eqs = eq0 & eq1 & eq2 &eq3
for t in range(1):
f0.updateOld()
f1.updateOld()
f2.updateOld()
f3.updateOld()
eqs.solve(dt = 1.0e-3)
viewer = Viewer((f0, f1, f2, f3))
Which results in the error:
fipy.terms.SolutionVariableNumberError: Different number of solution
variables and equations.
I believe that I am ignorant to something fundamental about FiPy and would
appreciate any guidance as to how to cast these equations in a form that
FiPy will take in.
~Dan
On Mon, Nov 24, 2014 at 1:35 PM, Daniel Wheeler <daniel.wheel...@gmail.com>
wrote:
> On Fri, Nov 21, 2014 at 12:08 PM, Dan Brunner <d...@brunnerd.com> wrote:
> > All,
> >
> > First, thanks for developing and supporting FiPy. I am just starting to
> > learn to use it with the hopes that it will become my standard tool for
> > solving PDEs.
>
> I hope it works out.
>
> > I've hit a bottle-neck in setting up my problem and cannot piece it all
> > together from the examples and FAQs.
>
> Have you tried solving for "mnv" as the independent variable and
> making "m" simply "mnv / (n * v)" assuming you need "m" for one of the
> P or S variables? That might work. You could also then try doing that
> as a fully coupled equation.
>
> These equiation have no diffusion terms so they will be hard to solve.
> Depending on what you're looking for in the solution, you really need
> Riemann coupling and high order advection terms, which FiPy doesn't
> currently have. Actually, there is no explicit coupling of the
> equations within the derivatives unless "P" has "n" dependence so
> Riemann does nothing.
>
> I probably need to see how your implementing things to be more helpful.
>
> --
> Daniel Wheeler
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>
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