HORSES3D: A high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics. We provide an overview of the high-order spatial discretisation (including energy/entropy stable schemes) and anisotropic p-adaptation capabilities. The solver is parallelised using MPI and OpenMP showing good scalability for up to 1000 processors. Temporal discretisations include explicit, implicit, multigrid, and dual time-stepping schemes with efficient preconditioners. Additionally, we facilitate meshing and simulating complex geometries through a mesh-free immersed boundary technique. We detail the available documentation and the test cases included in the GitHub repository.

我们介绍了高阶谱元求解器（High-Order Spectral Element Solver，缩写HORSES3D）的最新进展。该求解器是一款开源的高阶间断伽辽金（discontinuous Galerkin）框架，可用于求解各类流动问题，涵盖可压缩流动（含激波与无激波工况）、不可压缩流动、多种雷诺平均Navier-Stokes（Reynolds-Averaged Navier-Stokes，RANS）与大涡模拟（Large Eddy Simulation，LES）湍流模型、粒子动力学、多相流动以及气动声学问题。我们概述了该框架的高阶空间离散方法（包含能量/熵稳定格式）以及各向异性p自适应（anisotropic p-adaptation）功能。该求解器采用消息传递接口（Message Passing Interface，MPI）与开放多处理（Open Multi-Processing，OpenMP）实现并行化，在至多1000个处理器核心的部署规模下展现出优异的可扩展性。时间离散方案涵盖显式格式、隐式格式、多重网格（multigrid）格式以及对偶时间步进（dual time-stepping）格式，并配备高效预条件子。此外，我们通过无网格浸入边界技术，支持复杂几何构型的网格生成与仿真模拟。我们还详细介绍了该项目GitHub仓库中提供的官方文档与配套测试用例。