Bim package: Difference between revisions

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== 3D Time dependent problem ==
== 3D Time dependent problem ==


Here is an example of a 3D time-dependent Advection-Diffusion equation that uses <code> lsode </code>
Here is an example of a 3D time-dependent Advection-Diffusion equation that uses <code> lsode </code> for time-stepping.


The equation being solved is
The equation being solved is
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= 0 \qquad \mbox{ in } \Omega \times [0, T] =[0, 1]^3 \times [0, 1] </math>
= 0 \qquad \mbox{ in } \Omega \times [0, T] =[0, 1]^3 \times [0, 1] </math>


<math> \varphi = x + y - z </math>
<math> ~\varphi = x + y - z </math>


<math> - \left(.01 \nabla u - u \nabla \varphi \right)  \cdot \mathbf{n} = 0 </math>
<math> - \left(.01 \nabla u - u \nabla \varphi \right)  \cdot \mathbf{n} = 0  
\qquad \mbox{ on } \partial \Omega</math>


The initial condition is


<math> u = \exp (- \left(\frac{x-.2}{.2}\right)^2 - \left(\frac{y-.2}{.2}\right)^2 - \left(\frac{z-.2}{.2}\right)^2)</math>
<pre>
pkg load bim
x = linspace (0, 1, 40);
y = z = linspace (0, 1, 20);
msh = bim3c_mesh_properties (msh3m_structured_mesh (x, y, z, 1, 1:6));
nn = columns (msh.p);
ne = columns (msh.t);
x = msh.p(1, :).';
y = msh.p(2, :).';
z = msh.p(3, :).';
x0 = .2; sx = .1;
y0 = .2; sy = .1;
z0 = .8; sz = .1;
u = exp (- ((x-x0)/(2*sx)) .^2 - ((y-y0)/(2*sy)) .^2 - ((z-z0)/(2*sz)) .^2);
A = bim3a_advection_diffusion (msh, .01*ones(ne, 1), 100*(x+y-z));
M = bim3a_reaction (msh, 1, 1);
function du = f (u, t, A, M)
  du = - M \ (A * u);
endfunction
time = linspace (0, 1, 30);
lsode_options ("integration method", "adams");
U = lsode (@(u, t) f(u, t, A, M), u, time);
for ii = 1:1:numel (time)
  name = sprintf ("u_%3.3d", ii);
  delete ([name ".vtu"]);
  fpl_vtk_write_field (name, msh, {U(ii,:)', 'u'}, {}, 1);
endfor
</pre>
This is a video showing the .3 isosurface of the solution
[[Media:bim.avi]]


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[[Category:OctaveForge]]
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[[Category:Packages]]
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