An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes

An accurate conservative interpolation (remapping) algorithm is an essential component of most Arbitrary Lagrangian–Eulerian (ALE) methods. In this paper, we describe an efficient linearity and bound preserving method for polyhedral meshes. The algorithm is based on reconstruction, approximate integration and conservative redistribution. We validate our method with a suite of numerical examples, analyzing the results from the viewpoint of accuracy and order of convergence.