MPDATA remapping for unstructured meshes

Conservative interpolation (remapping), within arbitrary Lagrangian-Eulerian (ALE) schemes, requires the values of the scalar fluid variables to be interpolated from one computational mesh to one of differing geometry. Advection methods are commonly employed for the remapping step, in which fluxes are represented by over-lapping volumes between adjacent cells. In this work, a second-order, conservative, sign-preserving remapping scheme is developed using concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The non-oscillatory infinite gauge option of MPDATA is derived for remapping in volume co-ordinates and is based upon a general, compact and computationally efficient edge-based data structure, developed for use within an arbitrary finite volume framework [82]. For the first time, an MPDATA based remapping algorithm has been developed for ALE schemes for unstructured meshes which benefits from the inherent qualities of MPDATA i.e. multidimensionality, positive definiteness and second order accuracy. The extension of the Cartesian specific algorithm developed in [34], allows for the algorithm to operate on fully unstructured meshes, facilitating the application to a wider range of problems involving more complex geometries. The resulting increase in accuracy and symmetry of numerical solutions associated with the MPDATA based scheme is demonstrated using a multitude of numerical tests. The pro-posed approach utilises all available data in the calculation of anti-diffusive pseudo velocities in order to retain second-order accuracy and multidimensionality. Theoretical developments are supported by numerical testing and test cases are used to demonstrate the performance quality, accuracy, symmetry and multidimensionality of the MPDATA based finite volume remapping scheme.