针对三维高阶DG数值格式的智能激波捕捉方法研究

Investigation of intelligent shock-capturing method for three-dimensional high-order DG method

  • 摘要: 在计算流体力学领域,高阶间断伽辽金(high-order discontinuous Galerkin, DG)方法具有高阶精度、几何灵活性、自适应能力强和并行计算效率高等优势。然而,在使用高阶DG算法对高速流场进行数值模拟时,激波附近容易产生数值振荡,影响DG计算的稳定性。本文采用零样本学习的思想和图注意力机制模型,通过三维方波及其傅里叶级数展开构建样本集,并利用跨域迁移和图结构空间建模,实现了对三维算例激波附近数值振荡的高效抑制。通过对三维高速圆柱绕流、三维前台阶流动和三维半球绕流等算例的数值模拟,验证了在DG方法计算过程中嵌入本文构建的三维Gibbs现象智能去噪模型,能够有效消除激波附近的数值噪声,以智能化的方法实现了对激波附近数值振荡的抑制,保证了三维高阶DG的计算稳定性和激波捕捉精度。

     

    Abstract: In the field of computational fluid dynamics, the high-order discontinuous Galerkin(DG)method has the advantages of high-order format construction, geometric flexibility, adaptive calculation capability, and parallel computing efficiency. However, when the high-order DG algorithm is used to perform numerical simulation on the high-speed flow, numerical oscillations will occur near the shock wave, which will affect the stable progression of the DG calculation.This oscillation phenomenon is similar to the Gibbs noise in the field of image processing.With the development of modern science and technology, there are new ideas and options for using artificial intelligence methods to suppress numerical oscillations near shock waves.This paper proposes an intelligent denoising method for three-dimensional Gibbs phenomena to address the non-physical oscillation problem of high-order formats in the region near shock waves.In this paper, the idea of zero-shot learning and the graph attention model are adopted. Through cross-domain transfer and spatial modeling of graph structure, the high-efficiency suppression of numerical oscillations near the shock wave in three-dimensional cases is realized. numerically simulating the three-dimensional hypersonic cylindrical flow and three-dimensional forward step and three-dimensional hemisphere cases, it is verified that embedding the three-dimensional Gibbs phenomenon intelligent denoising model constructed this paper into the DG method calculation process can effectively eliminate the numerical noise near the shock wave, and the numerical oscillations near the shock wave are suppressed in an intelligent way, and the stability and shock wave capturing accuracy of the three-dimensional high-order DG are guaranteed.

     

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