论文标题
几何方法的新实现，用于求解Eady Slice方程
A new implementation of the geometric method for solving the Eady slice equations
论文作者
论文摘要
我们提出了Cullen＆Purser（1984）的几何方法的新实现，用于求解模拟大型大气流和额叶形成的半地球层状切片方程。几何方法是一种拉格朗日离散化，其中PDE由粒子系统近似。离散化的重要特性是它在节能。我们以半污染的最佳运输理论的语言重述了几何方法，并利用它来开发快速实施，将数值最佳运输理论的最新结果与一种新颖的自适应时间稳定方案相结合。我们的结果使Eady-Boussinesq垂直切片方程与它们的半缘近似之间进行了对比的比较。我们提供了进一步的证据表明，随着rossby数量趋向于零，随着Rossby数量往往为零，Eady-Boussinesq垂直切片方程的弱解会收敛到半地球形Eady Slice方程的弱解。
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The geometric method is a Lagrangian discretisation, where the PDE is approximated by a particle system. An important property of the discretisation is that it is energy conserving. We restate the geometric method in the language of semi-discrete optimal transport theory and exploit this to develop a fast implementation that combines the latest results from numerical optimal transport theory with a novel adaptive time-stepping scheme. Our results enable a controlled comparison between the Eady-Boussinesq vertical slice equations and their semi-geostrophic approximation. We provide further evidence that weak solutions of the Eady-Boussinesq vertical slice equations converge to weak solutions of the semi-geostrophic Eady slice equations as the Rossby number tends to zero.
