Abstract
A data transfer (called later remap) of physical fields between two meshes is an important step of arbitrary Lagrangian-Eulerian (ALE) simulations. This step is challenging for high-order discontinuous Galerkin schemes since the Lagrangian flow motion leads to high-order meshes with curved faces. It becomes even more challenging for unstructured polygonal meshes that do not have a polynomial map from the reference to a current cell. We propose and analyze a new framework to create remap schemes on curvilinear polygonal meshes based on the theory of virtual element projectors. We derive a conservative remap scheme that is high-order accurate in space and time. The properties of this scheme are studied numerically for smooth and discontinuous fields on unstructured quadrilateral and polygonal meshes.
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