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High-order polynomial reconstruction

Merged Stéphane Del Pino requested to merge feature/reconstruction into develop

Add polynomial reconstruction of arbitrary degree (as long as exact quadrature formula are available)

  • 1d, 2d and 3d are supported
  • use a generalized Horner like formula in any dimension (optimal evaluation)
  • reconstruction can be performed in parallel (number of ghost layers may have to be adjust with the --number-of-ghost-layers running option
  • symmetry boundary conditions are taken into account (on demand)
  • one is encourage to reconstruct multiple variables at once: it reduces considerably the cost

Three methods are available to evaluate the integration of the polynomial basis in the stencil

  • cell_center available for degree 1 reconstruction only. The most efficient,
  • element use element base quadrature formulas. Restricted to elements for which a conform transformation is defined
  • boundary use face based quadrature. Works for any polygonal cell and for any polytopal cell with triangle or quandragle faces (more expensive for low degrees).

Remains a bunch of developments:

  • propose new kind of stencils
    • stencils are by now too large (try to build "optimal" ones?
    • allow restriction to zones of stencils
  • define basic limitation strategies
  • give access to reconstruction options in pgs scripts.

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