Nektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in-situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enable more rapid on-boarding of new users unfamiliar with spectral/$hp$ element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments - in particular: the method of moving frames, which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a 'thick' strip model for the modelling of fluid-structure interaction problems in the context of vortex-induced vibrations. We conclude by commenting some directions for future code development and expansion.

中文翻译：

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Nektar++：增强高保真光谱/hp 元素方法的能力和应用

Nektar++ 是一个开源框架，它为使用高阶谱/$hp$ 元素方法开发偏微分方程求解器提供了一个灵活、高性能和可扩展的平台。特别是，Nektar++ 旨在克服通常与高阶方法相关的复杂实现挑战，从而使它们更容易在广泛的应用领域中使用。在本文中，我们介绍了与 Nektar++ 5.0 版相关的算法、实现和应用程序开发。我们描述了一些关键的软件和性能发展，包括我们在并行 I/O、原位处理、使用集体操作来开发当前和新兴硬件以及实现多解算器耦合的接口方面的策略。此外，我们提供了有关新开发的 Python 界面的详细信息，该界面使不熟悉光谱/$hp$ 元素方法、C++ 和/或 Nektar++ 的新用户能够更快速地入门。此版本还包含了许多数值方法的发展——特别是：移动框架的方法，它为嵌入式曲线流形和域上的方程的模拟提供了一种额外的方法；一种处理空间可变多项式阶数的方法；以及准 3D 模拟的新技术，允许在均匀方向上对几何结构进行空间变化的扰动。最后，我们演示了此版本中提供的新应用程序级功能，即： 用于生成高阶曲线网格的工具，称为 NekMesh；一种用于气动声学问题的新型 AcousticSolver；我们开发的“厚” 用于在涡激振动背景下对流固耦合问题进行建模的条带模型。最后，我们评论了未来代码开发和扩展的一些方向。