论文标题
准确无差异混合不连续的盖尔金方法，用于不可压缩的湍流
Exactly Divergence-free Hybrid Discontinuous Galerkin Method for Incompressible Turbulent Flows
论文作者
论文摘要
该论文涉及对不可压缩的湍流的H（DIV）融合杂种不连续的Galerkin离散化的研究。离散化方法提供了许多面向物理和解决方案的特性，这对于解决计算密集的湍流结构可能是有利的。还引入了具有众所周知的泰勒 - 霍德元素的Navier-Stokes方程的标准连续Galerkin离散化，以提供比较。解释了模拟湍流流的四个不同主要原理：雷诺平均的Navier-Stokes模拟，大型涡流模拟，变异多尺度方法和直接的数值模拟。大型的涡流模拟和变异多尺度在传统上困难的湍流案例计算中表现出了良好的希望。只有直接求解Navier-Stokes方程，才能超越这种准确性，但计算成本过高。非常普遍的策略是雷诺平均方法，因为它是最具成本效益的方法。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程测试案例进行了验证。所有数值测试均已使用有限元库NetGen/ngsolve进行。
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.
