Anisotropic Slope Limiting Techniques for Ocean Flow Simulation on Unstructured Meshes

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The goal of this project is the development of special limiting techniques for flow and transport with a particular focus on unstructured finite element ocean models. The proposed research will extend the approaches proposed and analyzed by the applicants in their previous work by adding capabilities tailored for the problem-specific anisotropy in geophysical applications. The new slope limiters will be able to distinguish between the horizontal and vertical parts of the discretization and limit those parts in a segregated manner in order to minimize the numerical diffusion introduced by the limiting procedure. In addition, we propose to extend the slope limiting procedure to vector fields - such as the flow velocity and diffusive fluxes. The numerical treatment of highly heterogeneous diffusion coefficients and nonlinear source terms will also be addressed when it comes to the design of positivity-preserving numerical algorithms for the vertical eddy viscosity turbulence model. The anisotropic flux correction schemes and slope limiters will be integrated into the software packages UTBEST3D and FESOM. A numerical study will be performed to quantify the amount of spurious mixing.