Conservative Rezoning (Remapping) for General Quadrilateral Meshes
Abstract
A classic problem in Lagrangian numerical hydrodynamics is the conservative transfer of quantities from an old, distorted mesh to a new mesh. The same problem arises whenever the mesh is changed as, for example, in adaptive mesh techniques. This transfer of information is an interpolation process which is frequently called rezoning (or remapping). The general problem of conservative rezoning from one arbitrary mesh to another may be formulated as follows: m _{k} = ∫∫∫ _{V k}ϱ( r) dV. That is, we compute the mass m_{k} of each cell of the new mesh by integrating the known density distribution in the old mesh over the cell volume V_{k}. A direct intregration is generally prohibitive. We show, however, that it is possible to convert this integral to a surface integral by the appropriate use of the divergence theorem, thus greatly reducing the complexity of the problem. For twodimensional general quadrilateral meshes the resulting method is exact and particularly simple.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1984
 DOI:
 10.1016/00219991(84)901256
 Bibcode:
 1984JCoPh..54..411D