GridapGeosciences.jl：一个用于一般流形上偏微分方程的Julia有限元软件包
GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds
- Monash University（莫纳什大学）
- Australian National University（澳大利亚国立大学）
- Bureau of Meteorology（气象局）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文介绍Julia软件包GridapGeosciences.jl，用于一般流形上的偏微分方程数值求解，基于网格细化和Gridap库，通过立方球面流形展示其在标量输运、热浅水方程和Boussinesq方程线性化中的应用。
AI中文摘要：
我们介绍了this http URL，这是一个新的并行分布式内存Julia软件包，用于在一般流形上对偏微分方程进行数值逼近。我们生成离散流形域的抽象方法依赖于一般的网格细化，并在Gridap有限元库中实现，其高级接口使得内蕴和外蕴变分公式的无缝定义成为可能。this http URL具有立方球面流形，本研究使用该流形来展示this http URL在不同应用中的功能。第一个应用涉及标量输运，我们开发了常见稳定化项的内蕴公式，这些公式被证明等价于众所周知的外蕴稳定化形式。这些稳定化项被用于开发二维热浅水方程的内蕴公式，其中包括迎风数值通量。最后一个应用是Boussinesq方程的线性化，我们展示了this http URL在三维流形上捕捉表面和垂直动力学的能力。
英文摘要：
We present GridapGeosciences$.$jl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstract approach to generating discrete manifold domains relies on mesh refinement in general, and is implemented within the Gridap finite element library, whose high-level interface enables seamless definition of both intrinsic and extrinsic variational formulations. GridapGeosciences$.$jl features the cubed sphere manifold, which is used in this study to showcase the functionality of GridapGeosciences$.$jl in different applications. The first application involves scalar transport where we develop intrinsic formulations of common stabilisation terms, which are shown to be equivalent to well-known extrinsic stabilisation formalisations. Such stabilisation terms are used to develop an intrinsic formulation of the two-dimensional thermal shallow water equations that includes upwinded numerical fluxes. The final application is a linearisation of the Boussinesq equations where we demonstrate the capacity of GridapGeosciences$.$jl to capture both surface and vertical dynamics on a three-dimensional manifold.
