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Center for Nonlinear Studies |
In most ALE numerical methods, a Lagrangian mesh is rezoned into a geometrically better mesh, then a conservative remapper (otherwise called projector) transfers the information from the Lagrangian mesh onto the rezoned one. In this work one considers the swept region remapper with no-connectivity change obtained by considering the region [AA'B'B] swept by one edge [AB] shared by cell 1 and 2. (Points A', B' are the rezoned locations of point A, B.) This swept region is associated with a donor cell (1 or 2) depending on the sign of the swept region. One then integrated the density field over the swept region to construct a mass flux between cell 1 and 2 due to the rezone process. Such a remapper has the huge advantage of being very simple, conservative by construction, working with general polygonal mesh and being extensible to 3D. However the two main drawbacks are: (A) mass flux is performed only across an edge: no mass flux does exist between two cells sharing only one vertex; (B) auto-intersection as it happens when the quadrangles [AA'B'B] is tangled is not well taken into account as the swept region is not correctly approximated in this case. We will present a cure to these drawbacks, keeping in mind two important points: -first, any improvement must be extensible in 3D, -second, direct calculation of intersection points/lines in 2D/3D must be avoided (as it is difficult/impossible to perform in general in 3D). Theoretical and numerical results will be presented.
Host: Mikhail Shashkov