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<p class="MsoNormal"><span lang="EN-US">Hi all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I would like to solve a two phase compressible flow using dune-fem. The equations I'm using are in
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">pressure/saturation form. <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">After finite volume spatial discretization I have the following system of ODEs to solve:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal">d/dt C(u(t)) = F(u(t)) + Q, <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">u = [P;S] // vector of pressures and saturations in each block<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">C = phi * rho(P) * S // Concentrations<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">F = fluxes<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Q = source terms<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I want to use the implicit euler method, then in each time step and in each iteration of the Newton solver<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I need to solve:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">[d/du C - dt d/du F] du = Residual<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Unfortunately from dune-fem tutorials I only found how to solve problems in the normal form<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">d/dt u(t) = F(u(t)) + Q <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">i.e. (Id: identity matrix)<o:p></o:p></span></p>
<p class="MsoNormal">[Id - dt d/du F] du = Residual<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">How could I solve my problem with dune-fem? Do you have any example?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I was thinking to add another operator “C_operator” in the odesolver and then change the newton function. But I’m not sure if it’s a good idea.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I would like to maintain compatibility with the dune-fem interface.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thanks,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> Andrea<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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