Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere
arXiv:1707.00855 · doi:10.1016/j.jcp.2018.08.027
Abstract
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity and layer depth, the discretisation has a diagnostic potential vorticity that satisfies a stable upwinded advection equation through a Taylor-Galerkin scheme; this provides a mechanism for dissipating enstrophy at the gridscale whilst retaining optimal order consistency. We also use upwind discontinuous Galerkin schemes for the transport of layer depth. These transport schemes are incorporated into a semi-implicit formulation that is facilitated by a hybridisation method for solving the resulting mixed Helmholtz equation. We illustrate our discretisation with some standard rotating sphere test problems.
arXiv commentaccepted version
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- A Mixed Mimetic Spectral Element Model of the Rotating Shallow Water Equations on the Cubed Sphere
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- Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
- The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods
- A Mixed Mimetic Spectral Element Model of the 3D Compressible Euler Equations on the Cubed Sphere
- Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphere
- Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements
- Sparse spectral and p-finite element methods for partial differential equations on disk slices and trapeziums
- Selective decay for the rotating shallow-water equations with a structure-preserving discretization