基于多矩有限体积法的壁面不可压缩湍流大涡模拟  

Large-eddy Simulation of Wall-bounded Incompressible Turbulent Flows Based on Multi-moment Finite Volume Method

作　　者：郝江旭 谢彬 HAO Jiangxu;XIE Bin(School of Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai,200240,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]上海交通大学海洋工程国家重点实验室,上海200240

出　　处：《中国造船》2024年第6期170-181,共12页Shipbuilding of China

基　　金：国家自然科学基金项目(12472293);上海市青年科技启明星计划项目(23QA1405000);上海交通大学特区计划项目(21TQ1400202)。

摘　　要：基于多矩有限体积法提出了一种用于非结构网格上壁面不可压缩湍流大涡模拟的数值模型。在该模型中,速度由体积分平均值(VIA)和节点值(PV)定义,并作为预测变量同步更新;压力定义为节点值,采用有限元方法进行计算。这种称作VPM-FEM的方法能达到三阶精度,不仅可以克服传统模型由于速度-压力失耦导致的数值稳定性问题,而且为大涡模拟提供了一种设计亚格子(SGS)模型的新数值框架。在此框架下开发了4种亚格子模型,在各自的插值模版上使用最小二乘法分别计算VIA和PV的涡黏度。与传统的有限体积法相比,此模型有效提高了大非正交非结构网格的数值稳定性,并极大降低了数值耗散,从而可以在相同网格分辨率下解析更精细的流动结构。另外,此模型在很大程度上抑制了数值解对亚格子模型的敏感性,降低了其对网格单元形状的依赖,对于具有高雷诺数和复杂几何形状的湍流问题可以实现高保真和稳健的数值模拟。The multi-moment based numerical model is proposed for performing large-eddy simulation(LES)of wall-bounded incompressible turbulent flows on the unstructured grids.In this model,velocity is defined as volume integral average(VIA)and point values(PV)which are updated as prognostic variables simultaneously in time.Using VIA and PV in each cell,this method constructs higher-order polynomial on a compact stencil and more importantly,provides a new approach to design subgrid-scale(SGS)models for LES.Various SGS models are developed in this framework where the eddy-viscosity is computed separately at both VIA and PV using the least-square method on different interpolation stencils.Compared with conventional finite volume schemes,the proposed method effectively reduces numerical dissipation and largely suppresses the sensitivity of numerical solution on SGS models and resolves more elaborated flow structures on the same mesh resolution.It also reduces solution dependence on the shape and quality of grid elements,as demonstrated by comparing numerical results on the different types of grids.The proposed method can attain high-fidelity simulation without loss of numerical efficiency and robustness,which is highly appealing for complex turbulent problems with high Reynolds numbers and complicated geometries.

关 键 词：多矩有限体积法 壁湍流 亚格子模型 高雷诺数 大涡模拟 

分 类 号：O35[理学—流体力学]