NekMesh: An open-source high-order mesh generation framework

High-order spectral element simulations are now becoming increasingly popular within the computational modelling community, as they offer the potential to deliver increased accuracy at reduced cost compared to traditional low-order codes. However, to support accurate, high-fidelity simulations in complex industrial applications, there is a need to generate curvilinear meshes which robustly and accurately conform to geometrical features. This is, at present, a key challenge within the mesh generation community, with only a few open-source tools able to generate curvilinear meshes for complex geometries. We present NekMesh: an open-source mesh generation package which is designed to enable the generation of valid, high-quality curvilinear meshes of complex, three-dimensional geometries for performing high-order simulations. We outline the software architecture adopted in NekMesh, which uses a pipeline of processing modules to provide a flexible, CAD-independent high-order mesh processing tool, capable of both generating meshes for a wide range of use cases, as well as post-processing linear meshes from a range of input formats for use with high-order simulations. A number of examples in various application areas are presented, with a particular emphasis on challenging aeronautical and fluid dynamics test cases.

当前，高阶谱元模拟在计算建模领域愈发流行，相较于传统低阶求解代码，其具备以更低计算成本实现更高精度的潜力。然而，为支撑复杂工业场景下的高精度、高保真模拟，亟需生成能够稳健且精准贴合几何特征的曲线网格。目前，这仍是网格生成领域的核心挑战之一，仅有少量开源工具可针对复杂几何模型生成曲线网格。本文提出NekMesh：一款开源网格生成工具包，专为高阶模拟设计，可用于生成复杂三维几何模型的合法、高质量曲线网格。本文详述了NekMesh所采用的软件架构：其通过由多个处理模块构成的流水线，打造了灵活且不依赖计算机辅助设计（CAD，Computer Aided Design）的高阶网格处理工具，既可面向多样化应用场景生成网格，也可对多种输入格式的线性网格进行后处理，以适配高阶模拟需求。本文还展示了多个不同应用领域的案例，尤其着重介绍了极具挑战性的航空航天与流体动力学测试场景。