Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes
Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes
复制标题
非结构化网格上可压缩流的混合不连续伽辽金有限体积技术
DOI：
10.1016/j.jcp.2022.111755
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发表时间：
2023
影响因子：
4.1
通讯作者：
Maltsev V
中科院分区：
文献类型：
--
作者：
Maltsev V
在本文中，我们发展了一族任意高阶、无振荡的间断Galerkin(DG)-有限体积(FV)格式，用于混合单元非结构网格。它们的关键成分是当通过检查无限DG解的故障小区指示器检测到无效解时，在DG方法和基于CWENOZ方案的FV方法之间切换。因此，DG提供的高阶精度在计算域的平滑区域被保留，而FV的稳健性在强梯度区域被利用。所使用的高阶CWENOZ变量具有与DG变量相同的空间精度阶数，同时代表了非结构网格上最紧凑的应用之一，因此简化了实现，减少了与原始WENO重建的大模板相关的计算开销，而不牺牲格式所希望的无振荡特性。我们仔细研究了与DG和FV方法之间的切换相关的几个参数，包括预先考虑的问题单元指示器。在文献中，我们第一次研究了可允许解的界的定义，我们使用问题胞元指示符的频率，以及非稳定测试问题的问题胞元百分比的演化。对已有的试验问题求解了二维和三维欧拉方程，并与计算或实验参考解进行了比较。所有方法都已在UCNS3D开源高阶非结构化计算流体动力学(CFD)解算器中实现和部署。这种耦合有可能以计算效率的方式改进FV-DG的缺点。改进的精度和稳健性对于工业规模的CFD应用来说是非常重要的特征，并且有利于扩展到其他控制方程系统。
In this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Discontinuous Galerkin(DG)-Finite Volume(FV) schemes for mixed-element unstructured meshes. Their key ingredient is a switch between a DG method and a FV method based on the CWENOZ scheme when invalid solutions are detected by a troubled cell indicator checking the unlimited DG solution. Therefore, the high order of accuracy offered by DG is preserved in smooth regions of the computational domain, while the robustness of FV is utilized in regions with strong gradients. The high-order CWENOZ variant used has the same spatial order of accuracy as the DG variant, while representing one of the most compact applications on unstructured meshes, therefore simplifying the implementation, reducing the computational overhead associated with large stencils of the original WENO reconstruction without sacrificing the desirable non-oscillatory properties of the schemes. We carefully investigate several parameters associated with the switching between DG and FV methods including the troubled cell indicators ina priorifashion. For the first time in the literature, we investigate the definition of the bounds for an admissible solution, the frequency by which we use the troubled cell indicators, and the evolution of the percentage of troubled cells for unsteady test problems. The 2D and 3D Euler equations are solved for well established test problems and compared with computational or experimental reference solutions. All the methods have been implemented and deployed within theUCNS3Dopen-source high-order unstructured Computational Fluid Dynamics (CFD) solver. The present coupling has the potential to improve the shortcomings of both FV-DG in a computational efficient manner. The improved accuracy and robustness provided is a characteristic of paramount importance for industrial-scale CFD applications, and favours the extension to other systems of governing equations.