Towards isotropic transport with co-meshes

Transport is the central ingredient of all numerical schemes for hyperbolic partial differential equations and in particular for hydrodynamics. Transport has thus been extensively studied in many of its features and for numerous specific applications. In more than one dimension, it is most commonly plagued by a major artifact: mesh imprinting. Though mesh imprinting is generally inevitable, its anisotropy can be modulated and is thus amenable to significant reduction. In the present work we introduce a new definition of stencils by taking into account second nearest neighbors (across cell corners) and call the resulting strategy co-mesh approach. The modified equation is used to study numerical dissipation and tune enlarged stencils in order to minimize transport anisotropy.