In recent years Computational Fluid Dynamics (CFD) has become a widespread practice in industry. The growing need to simulate off-design conditions, characterized by massively separated flows, strongly promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the Large Eddy Simulation (LES), to an industrial level. Among the possible approaches to the SRS, an appealing choice is to perform Implicit LES (ILES) via a high-order Discontinuous Galerkin (DG) method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. To reduce the large CPU time for ILES, implicit time integrators, that allows for larger time steps than explicit schemes, can be considered. The main drawbacks of implicit time integration in a DG framework are represented by the large memory footprint, the large CPU time for the operator assembly and the difficulty to design highly scalable preconditioners for the linear solvers. In this paper, which aims to significantly reduce the memory requirement and CPU time without spoiling the high-order accuracy of the method, we rely on a p-adaptive algorithm suited for the ILES of turbulent flows and an efficient matrix-free iterative linear solver based on a cheap p-multigrid preconditioner and a Flexible GMRES method. The performance and accuracy of the method have been assessed by considering the following test cases: (1) the T3L test case of the ERCOFTAC suite, a rounded leading edge flat plate at $${\mathrm{Re}}_D=3450$$ ; (2) the flow past a sphere at $$\mathrm{Re}_D=300$$ ; (3) the flow past a circular cylinder at $$\mathrm{Re}_D=3900$$ .

中文翻译：

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不可压缩过渡流的隐式 LES 的 p 自适应无矩阵不连续 Galerkin 方法

近年来，计算流体动力学 (CFD) 已成为工业中的广泛实践。对以大量分离流动为特征的非设计条件进行仿真的需求日益增长，这有力地促进了模型和方法的研究，以提高计算效率并带来尺度解析模拟 (SRS) 的实践，如大涡模拟 (LES)，达到工业水平。在 SRS 的可能方法中，一个有吸引力的选择是通过高阶不连续伽辽金 (DG) 方法执行隐式 LES (ILES)，其中空间离散化方案的有利数值耗散直接起到亚网格尺度的作用模型。为了减少 ILES 的大量 CPU 时间，可以考虑隐式时间积分器，它允许比显式方案更大的时间步长。DG 框架中隐式时间积分的主要缺点表现为内存占用量大、操作符组装的 CPU 时间长以及难以为线性求解器设计高度可扩展的预处理器。在本文中，旨在在不破坏该方法的高阶精度的情况下显着减少内存需求和 CPU 时间，我们依赖于适用于湍流 ILES 的 p 自适应算法和高效的无矩阵迭代线性求解器基于廉价的 p-multigrid 预处理器和灵活的 GMRES 方法。该方法的性能和准确性已通过考虑以下测试用例进行评估：（1）ERCOFTAC套件的T3L测试用例，圆形前缘平板在$${\mathrm{Re}}_D=3450$$ ; (2) 在 $$\mathrm{Re}_D=300$$ 处流过一个球体；