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首页> 外文期刊>Journal of Computational Physics >A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
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A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

机译：用于3D不可压缩流量的高阶半明确的不连续的Galerkin求解器，适用于DNS和湍流通道流量的应用

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Abstract We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier–Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad–div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at R e τ = 180 as well as 590. ]]>
机译：<！[cdata [ Abstract 我们提出了一种有效的不连续的Galerkin方案，用于模拟加不可压缩的Navier-Stokes方程，包括层流和湍流。我们考虑一个半显式的高阶速度校正方法，用于时间集成以及用于速度和压力的节点等单位离散化。非线性对流术语是明确处理的，同时为压力泊松方程和粘性术语求解线性系统。我们的解决者的关键特征是减少局部发散误差的一致惩罚术语，以克服最近在空间欠下的高雷诺数流量以及较小的时间步骤中报告的稳定性。这种惩罚方法类似于广泛用于连续有限元的渐变稳定。我们进一步审查并比较了我们在文献中提出的几种其他技术的方法，以稳定这种流量配置的方法。通过矩阵线性求解器专门设计用于大规模计算，包括矩阵的线性求解器，包括有效的预处理策略和张量 - 产品元素，这些元素使我们能够将该代码扩展到3440亿度自由和147,456个CPU核心。我们验证了我们的代码，并展示了涡流问题中存在的层流量的最佳收敛速率，并将汽缸流过流动并显示了我们的求解器的适用性直接数值模拟，以及 r E τ = 180 以及590。 ]]>

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