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I am looking for Finite Volume Software that employs a method-of-lines like approach by constructing from the hyperbolic PDE of form $$\partial_t \boldsymbol u(t,\boldsymbol x) + \nabla \cdot \boldsymbol f\big(\boldsymbol u(t,\boldsymbol x)\big) = \boldsymbol 0 \tag{1} $$ the semidiscretized ODE $$ \frac{d }{d t} \boldsymbol U(t) = \boldsymbol F\big(\boldsymbol U(t)\big) \tag{2} \label{2} $$ and allows the computation of the Jacobian of the RHS of \eqref{2}:

$$ J(\boldsymbol u) = \nabla_{\boldsymbol u} \boldsymbol F (\boldsymbol u) $$

Preferably, this is done with algorithmic/automatic differentiation, although finite differences should also be alright for the beginning. Also, computation for the initial value $\boldsymbol u_0$ would also suffice here.

I checked standard software like Clawpack and FiPy but they do not seem to offer such capabilities.

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  • $\begingroup$ If DG is an acceptable substitute then I can recommend things but I don't know anything for finite volume :/ $\endgroup$
    – Daniel Shapero
    Dec 20, 2022 at 15:28
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    $\begingroup$ @Daniel Shapero Does your recommendation supports polynomial degrees $P=0$? Could be accepted as an answer. $\endgroup$
    – ConvexHull
    Dec 20, 2022 at 17:36
  • $\begingroup$ I am particularly NOT asking for DG - although zero'th order polynomials would be a starting point $\endgroup$
    – Dan Doe
    Dec 20, 2022 at 23:43
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    $\begingroup$ github.com/SciML/MethodOfLines.jl has PDE support in progress, but you also can always hand convert the system. It's not yet ideal for PDE's but it will give you AD for free. $\endgroup$
    – Oscar Smith
    Dec 23, 2022 at 2:57
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    $\begingroup$ MethodOfLines.jl does WENO schemes. $\endgroup$
    – Chris Rackauckas
    Dec 25, 2022 at 19:14

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