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<p>Hello, I want to set a TS object for the time integration of my
FV CFD solver.</p>
<p>The equation is M dQ/dt = f(Q) where M is a diagonal mass matrix
filled with the cell volumes from my FV discretisation. I've read
the PETSc manual and I found some interesting mails in the
petsc-users archive, but I still do not understand something.</p>
To me, there is three ways I could set my TS :<br>
<blockquote><tt>1. F(t, x, x') = Mx' - f(x) and G(t, x) = 0
(default)</tt><tt><br>
</tt><tt>2. F(t, x, x') = Mx' and G(t, x) = f(x)</tt><tt><br>
</tt><tt>3. F(t, x, x') = x' (default) and G(t, x) = M^{-1} f(x)</tt></blockquote>
<p>From
(<a class="moz-txt-link-freetext" href="https://lists.mcs.anl.gov/pipermail/petsc-dev/2017-October/021545.html">https://lists.mcs.anl.gov/pipermail/petsc-dev/2017-October/021545.html</a>),
I think that unless I'm using an IMEX method, whatever F and G, it
does F <-- F - G internally, but I would like to be sure.<br>
</p>
<p><br>
</p>
<p>Will there be a difference be if I use an explicit method, as
Euler or RK ? What about implicit method such as BEuler or Theta
methods ?</p>
<p>If I use an implicit method (beuler), what happens if I don't
give F' and/or G' ? Are their matrix-vector product approximated
with finite difference ?<br>
</p>
<p>What I understand is that for implicit-explicit methods, "G is
treated explicitly while F is treated implicitly". In this case,
am I right to assume it's useless to give the RHS Jacobian ? Then,
when is G' used ?</p>
<p>If I do not use an IMEX method, are the 3 formulations equivalent
?</p>
<p><br>
</p>
<p>Thank you for your help</p>
<p><br>
</p>
<p>Pierre Seize<br>
</p>
<p><br>
</p>
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