High-Order Conservative Remapping with a posteriori MOOD stabilization on polygonal meshes
Résumé
In this article we present a 2D conservative remapping method which relies on exact polygonal mesh in-
tersection, high accurate polynomial reconstruction (up to degree 5) and a posteriori stabilization based on
MOOD paradigm [21, 30, 31, 80]. This paradigm does not compute any sort of a priori limiter for the poly-
nomial reconstructions. Instead it rather observes if the candidate solution after remapping does not fulfill
user-given validity criteria, and, in this case, locally to those so-called problematic cells, the method decre-
ments the polynomial degree for the reconstructions. These problematic cells are then recomputed starting
from lower order accurate polynomial representations on the old mesh. Next, the candidate remapped so-
lution in these cells is again tested against the validity criteria and, possibly, some degree decrementation
is applied once again. Such iterative procedure always ends either with a valid remapped solution obtained
from polynomial degree greater than 0, or, in the worst case scenario, with a formally first order accurate
remapped cell remapped (without any polynomial reconstruction). Numerical results assess the behavior
of such remapping method on pure remapping problems of scalar quantity (smooth and discontinuous) and
on some emulation of system of hydrodynamics equations for which interleaved variables are considered
(mass, momentum and energy) along with physical constraints (positivity of density and pressure).
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