hamilton-jacobi / level-set equations

I am interested in a DG solver for hamilton-jacobi equations (of the form $`\varphi_t + H(\nabla \varphi) = 0`$) as they arise in level-set methods (e.g. $`H(\nabla \varphi) = a \| \nabla \varphi \|`$ for movement normal to the level-set interface or $`H(\nabla \varphi) = \bf{v} \nabla \varphi`$ for movement with an external velocity field or any linear combination of these or similar operators).

There are DG methods for this type of equation (e.g. https://www.sciencedirect.com/science/article/abs/pii/S0021999110005255 where auxiliary variables for the spatial derivatives are introduced and numeric fluxes are defined for these). Can this this kind of method be implemented in the Trixi framework? Are you aware of other options?

I'm sorry for not being very well versed in DG methods. Appreciate any help you can provide.

The issue names no Trixi files, tests, or entry points. Start by reviewing existing DG solver implementations and the referenced Hamilton-Jacobi DG method, then determine the required formulation and validation cases; done would mean an agreed implementation scope with tests demonstrating the solver.

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