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：我们建议,基于DG空间分解和TR-BDF2时间分解方法,为压抑性纳维埃-斯托克斯方程式提供一个高效、准确和稳健的隐含求解器,该方法的效力体现在一些古典基准中,这些基准突出显示了它相对于广泛使用的其他隐含方法而言的超高效率。 在协议框架内平行实施拟议方法。 II 软件包可以在复杂的地貌中进行准确和高效的适应模拟,从而使拟议的求解器对大规模工业应用具有吸引力。