We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely used implicit approaches. The parallel implementation of the proposed method in the framework of the deal.II software package allows for accurate and efficient adaptive simulations in complex geometries, which makes the proposed solver attractive for large scale industrial applications.

翻译：本文提出一种基于DG空间离散化与TR-BDF2时间离散化方法的高效、精准且鲁棒的不可压缩Navier-Stokes方程隐式求解器。通过一系列经典基准算例验证了该方法的有效性，结果表明其相较于其他广泛使用的隐式方法具有显著更高的计算效率。基于deal.II软件框架实现的并行计算版本，可对复杂几何区域开展高精度高效率的自适应模拟，使该求解器在大规模工业应用中具有显著吸引力。