This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be advantageous for resolving computationally intensive turbulent structures. A standard continuous Galerkin discretization for the Navier-Stokes equations with the well-known Taylor-Hood elements is also introduced in order to provide a comparison. The four different main principles of simulating turbulent flows are explained: the Reynolds-averaged Navier-Stokes simulation, large eddy simulation, variational multiscale method and the direct numerical simulation. The large eddy simulation and variational multiscale have shown good promise in the computation of traditionally difficult turbulent cases. This accuracy can be only surpassed by directly solving the Navier-Stokes equations, but comes with excessively high computational costs. The very common strategy is the Reynolds-average approach, since it is the most cost-effective. Those modelling principles have been applied to the two discretization techniques and validated through the basic plane channel flow test case. All numerical tests have been conducted with the finite element library Netgen/NGSolve.

中文翻译：

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不可压缩湍流的完全无散度混合不连续伽辽金方法

本论文涉及不可压缩湍流的符合 H(div) 的混合不连续 Galerkin 离散化的研究。离散化方法提供了许多物理和面向求解的属性，这可能有利于解析计算密集型湍流结构。为了提供比较，还引入了具有众所周知的 Taylor-Hood 元素的 Navier-Stokes 方程的标准连续 Galerkin 离散化。解释了模拟湍流的四种不同的主要原理：雷诺平均 Navier-Stokes 模拟、大涡模拟、变分多尺度方法和直接数值模拟。大涡模拟和变分多尺度在传统困难湍流情况的计算中显示出良好的前景。这种精度只能通过直接求解 Navier-Stokes 方程来超越，但计算成本过高。非常常见的策略是雷诺平均法，因为它最具成本效益。这些建模原理已应用于两种离散化技术，并通过基本平面通道流测试用例进行了验证。所有数值测试均使用有限元库 Netgen/NGSolve 进行。