A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods
A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods
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DOI：
10.1016/j.cma.2021.113820
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Edward Laughton;G. Tabor;D. Moxey
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文献类型：
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作者：
Edward Laughton;G. Tabor;D. Moxey
在模型中整合移动几何特征以进行复杂模拟的能力是许多领域的常见要求。例如，航空应用中的流体力学通常具有旋转（例如涡轮、轮子和风扇叶片）或滑动部件（例如在压缩机或涡轮叶栅模拟中）的特征。随着这些情况的高保真度建模趋势不断增加，特别是与高阶不连续伽辽金方法相结合，因此需要了解静态网格和滑动/旋转部件之间的界面的不同数值处理如何影响整体解决方案质量。在本文中，我们比较了处理这种非共形接口的两种不同方法。第一种是所谓的砂浆方法，其中沿边缘的通量积分根据非共形网格的定位进行分割。第二种是文献较少的点对点插值方法，其中用于通量评估的内部和外部量是从位于界面相对侧的元素插值的。尽管迫击炮方法在数值属性方面具有显着优势，因为它保留了 DG 方法的局部守恒属性，但在复杂的 3D 网格背景下，它带来了显着的实现困难，而点对点方法更容易处理这些困难。在本文中，我们研究了每种方法的数值特性，不仅关注观察平滑解的收敛阶，还关注每种方法在线性和非线性双曲问题的欠解析模拟中的表现，以便为这些方法在隐式大涡模拟中的使用提供信息。
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations.