Anisotropic Slope Limiting Techniques for Ocean Flow Simulation on Unstructured Meshes

该项目的目标是开发流动和运输的特殊限制技术，特别侧重于非结构有限元海洋模型。拟议的研究将扩展申请者在他们以前的工作中提出和分析的方法，增加为地球物理应用中特定问题的各向异性量身定做的能力。新的斜率限制器将能够区分离散的水平和垂直部分，并以分离的方式限制这些部分，以便最大限度地减少限制程序引入的数值扩散。此外，我们还建议将斜率限制法推广到矢量场，如流速和扩散通量。在设计垂直涡粘性湍流模式的保正数值算法时，还将讨论高度非均匀扩散系数和非线性源项的数值处理。各向异性通量校正方案和斜率限制器将被集成到软件包UTBEST3D和FESOM中。将进行数值研究，以量化杂散混合量。

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.