No abstract

An arbitrary finite volume approach is developed for discretising partial differential equations governing fluid flows on the sphere. Unconventionally for unstructuredmesh global models, the governing equations are cast in the anholonomic geospherical framework established in computational meteorology. The resulting discretisation retains proven properties of the geospherical formulation, while it offers the flexibility of unstructured meshes in enabling irregular spatial resolution. The latter allows for a global enhancement of the spatial resolution away from the polar regions as well as for a local mesh refinement. A class of non-oscillatory forward in time edge-based solvers is developed and applied to numerical examples of threedimensional hydrostatic flows, including shallow-water benchmarks, on a rotating sphere.

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small-and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.

No abstract