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Add 2D flow models with DG discretization #251

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@jbreue16

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@jbreue16

A DG implementation of the 2D interstitial column flow is a promising extension as the performance advantage of DG compared to lower order methods scales with the number of DoF.

To do

  • MS1: Add a DG discretization for a 2D LRMP with spatially constant parameters #160
  • MS2: Add piece-wise constant radial dependence of parameters to 2D DG discretization #337
  • MS3: add the 2D GRM with DG
  • MS4: Clean-up and finish loose ends
    • more tests?
    • documentation; optimally not repetetive but modular for the 2D models
    • Flow rates issue (a sanity check is added in Add piece-wise constant radial dependence of parameters to 2D DG discretization #337 to make sure velocities are constant within each radial element)
    • Export solution for nodal averaged radial zones instead of exact values at nodes? the averages would be required anyways with the current implementation, for the connection of other units at the outlet.
    • recompute operators on section transitions
    • Fix radial coordinate inaccuracies: Ive observed a coordinate $R^c$ by some $1E-18$.. maybe fix the last coordinate to be exact?
    • consistent initialization with AD Jacobian and req binding fails
  • MS5: Further improvements
    • enable variable polynomial degree per radial element?
    • Parallelization
    • improve AD Jacobian seeding by using block-wise dense AD and reduce default AD directions accordingly (see Jacobian tests)
    • backwards flow
  • MS6: add the 2D LRM with DG
  • MS7: Explore, if we should and can resolve arbitraryly radially dependent parameters
    • arbitrary order Gauss quadrature?
    • fully radially dependent axial and radial dispersion
    • piece-wise constant flow rates; are fully radially dependent porosity, velocity possible/worth the effort?

wont fix for now: Handle sensitivities for parameters that are included in operators (issue with that is described in #214 ): column radius, radial and axial dispersion

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