Towards an unstructured-mesh all-scale atmospheric model

A rigid connectivity of Cartesian grid routinely used in the simulation of stratified rotating flows imposes severe limitations on mesh adaptivity to flow features and/or the complex geometry of physical domains. In contrast, for many problems, a wide range of scales in atmospheric flows, heterogeneous distribution of regions of interest, and/or complex geometry can be accommodated efficiently with fully unstructured-mesh technology. The realization of limitations of structured grids, and of a need for flexible mesh adaptivity, has stimulated recent interest within the atmospheric/oceanic science community in the development of unstructured-mesh solvers. However, such solvers are still in their infancy compared to both established structured-grid codes and state-of-the-art engineering advancements with unstructured meshes. In order to prove the competence and competitiveness of unstructured-mesh technology for simulating all-scale flows in the atmosphere and oceans, there is a need for developing an advanced fully non-hydrostatic model for simulating accurately rotating stratified flows in a broad range of the Rossby, Froude, and Reynolds-number regimes. The seminar will report on recent work aiming at this goal.
A brief discussion of point, edge and element data structures --most commonly used in finite difference, volume and element discretisation-- will illustrate the generality and accuracy benefits associated with the edge-based unstructured meshes formulation, emphasizing its ability to handle arbitrary polyhedral meshes and a range of mesh adaptivity techniques. The essential steps leading towards a fully non-hydrostatic model such as a development of accurate advection schemes and a class of non-oscillatory forward-in-time solvers will be described. A generalization to algorithms operating on a sphere will follow.
The key of the present development is a derivation of approach which provides a simple equivalence between the structured grid methodologies used in EULAG and the edge-based framework.Consequently, the proven elements of the EULAG’s non-hydrostatic model translate directly to unstructured meshes. This not only provides a particularly efficient numerical development path, but also facilitates a meaningful comparison between the performance of structured and unstructured meshes.