Hi John,
Thank you for your answer. Just to clarify that the mesh is static throughout
time, so old_solution would be stored in terms of the coordinates
$\mathbf{x}^{j+1}$. I want to find out the old_solutions at the points
$((\delta t) \mathbf{u}^{j+1} + \mathbf{x}^{j+1})$ so i can evaluate the
solution using the method of characteristics. I know how to do this using my
own FE code, but I've failed to work out how to implement it in deal.ii.
Hope that makes sense?
Katie
________________________________
From: John Chapman [[email protected]]
Sent: 04 April 2011 14:48
To: Katie Leonard
Cc: [email protected]
Subject: Re: [deal.II] Solving extension of Step-21 using method of
characteristics
Hi Katie,
If you have refinement then you should try SolutionTransfer (which is covered
in several of the tutorial examples, step-15 first of all). If not can you
just save the old solution at the end of the do...while timestep loop and then
use fe_values.get_function_values(old_solution, old_solution_values)?
If I have misunderstood your question, please clarify!
John
John Chapman
www.maths.dur.ac.uk/~tphj28<http://www.maths.dur.ac.uk/~tphj28>
On 04/04/11 14:31, Katie Leonard wrote:
Hello everyone,
I am new to Deal.ii and I am having an issue implementing a problem, which is
an extension of step-21. To iterate through time I am solving the equation
(which is analogous to the saturation equation in step-21):
$\frac{\partial C}{\partial t} + \mathbf{u} \cdot \nabla C = F(C, \mathbf{u}) +
\nabla^2 C$
given $\mathbf{u}$ and $C(0)$. For stability purposes, we solve this using the
method of characteristics i.e.
$\frac{\mathrm{d} C}{\mathrm{d} t} = F(C, \mathbf{u} ) + \nabla^2 C $
on the line
$\frac{\mathrm{d} \mathbf{x} }{\mathrm{d} t} = \mathbf{u}$
and discretising time (with timestep \delta t) gives:
$\frac{C^{j+1} - C^j}{\delta t} = F(C^{j+1}, \mathbf{u}^{j+1} ) + \nabla^2
C^{j+1} $
on
$\frac{ \mathbf{x}^{j+1} - \mathbf{x}^j }{\delta t} = \mathbf{u}^{j+1}$
So,
$\frac{C^{j+1}(\mathbf{x}^{j+1} ) - C^j ((\delta t) \mathbf{u}^{j+1} +
\mathbf{x}^{j+1}) }{\delta t} = F(C^{j+1}(\mathbf{x}^{j+1} ) ,
\mathbf{u}^{j+1}(\mathbf{x}^{j+1} ) ) + \nabla^2 C^{j+1} (\mathbf{x}^{j+1} ) $
My problem is that, at each timestep I need to be able to find out the previous
solution for C at the points on the domain $((\delta t) \mathbf{u}^{j+1} +
\mathbf{x}^{j+1})$ to give the solution C^{j+1}(\mathbf{x}^{j+1} )
Many thanks,
K L
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