用于海岸适应无结构双元网格上的准地转方程的保守有限体积方案
Conservative finite volume schemes for the quasi-geostrophic equation on coastal-conforming unstructured primal-dual meshes
AI总结：
本文提出了解决无粘性和有粘性准地转方程的有限体积方案，采用海岸适应无结构双元网格，并探讨了几种强制边界条件的方法。这些方案中的纯传输部分在平均意义上保持了潜涡量，并在时间截断误差内保持了潜涡量。通过基于质心Voronoi-Delaunay网格的数值测试来验证这些性质，并区分这些方案的动力学行为。最后讨论了这些方案在不同情况下的潜在应用。
摘要：
在本文中，我们提出了解决无粘性和有粘性准地转方程的有限体积方案，采用海岸适应无结构双元网格。同时，也探讨了几种强制边界条件的方法。这些方案中的纯传输部分在平均意义上保持了潜涡量，并在时间截断误差内保持了潜涡量。基于质心Voronoi-Delaunay网格的数值测试用于验证这些性质，并区分这些方案的动力学行为。最后讨论了这些方案在不同情况下的潜在应用。
英文摘要：
In this paper we propose finite volume schemes for solving the inviscid and viscous quasi-geostrophic equations on coastal-conforming unstructured primal-dual meshes. Several approaches for enforcing the boundary conditions are also explored along with these schemes. The pure transport part in these schemes are shown to conserve the potential vorticity along fluid paths in an averaged sense, and conserve the potential enstrophy up to the time truncation errors. Numerical tests based on the centroidal Voronoi-Delaunay meshes are performed to confirm these properties, and to distinguish the dynamical behaviors of these schemes. Finally some potential applications of these schemes in different situations are discussed.
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