Hello all,
I've written generic, implicit HDG/DG solvers that solve a second-order
diffusion type equation $\frac{du}{dt} - \nabla^2 u = f$ (where f is a
generic DG finite element field). As I'm expanding the code to a set of
projection methods, I'd like this $f$ to represent an explicitly computed
advection term on the right-hand side $\nabla\cdot (u^k \otimes u^k)$ at
time $k+1$.
I'd like to assemble the weak form of the advection term, something like
$-(∇v, u^k\otimes u^k)_K +(v, F^*(u)\cdot n)_{\partial K}$ (where F^*(u) is
the convective numerical flux) on the right hand side for every element K
and store that as a DG field. To avoid breaking the abstraction of the
implicit solver classes, is it possible to compute this term outside the
main solver classes and pass it in as a DG Field represented as a
Vector<double>?
I suspect this can be done, but I'm unsure how to populate a Vector<double>
directly with terms like these, since there's no global assembly to be
done. Perhaps it can be filled directly with MeshWorker::mesh_loop?
Any advice would be appreciated!
Corbin
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