Purpose

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the hyperbolic conservation law. However, it requires a significant amount of computing resources. Therefore, this paper aims to investigate how to solve the Euler equations in parallel systems and improve the parallel performance.

Design/methodology/approach

Discontinuous Galerkin discretization is used for the compressible inviscid Euler equations. The multi-level domain decomposition strategy was used to deal with the computational grids and ensure the calculation load balancing. The total variation diminishing (TVD) Runge–Kutta (RK) scheme coupled with the multigrid strategy was employed to further improve parallel efficiency. Moreover, the Newton Block Gauss–Seidel (GS) method was adopted to accelerate convergence and improve the iteration efficiency.

Findings

Numerical experiments were implemented for the compressible inviscid flow problems around NACA0012 airfoil, over M6 wing and DLR-F6 configuration. The parallel acceleration is near to a linear convergence. The results indicate that the present parallel algorithm can reduce computational time significantly and allocate memory reasonably, which has high parallel efficiency and speedup, and it is well-suited to large-scale scientific computational problems on multiple instruction stream multiple data stream model.

Originality/value

The parallel DGFEM coupled with TVD RK and the Newton Block GS methods was presented for hyperbolic conservation law on unstructured meshes.

中文翻译：

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非结构网格上双曲守恒律的并行不连续Galerkin有限元方法

目的

不连续的Galerkin有限元方法（DGFEM）非常适合在非结构化网格上实现高阶分辨率近似，以计算双曲守恒律。但是，它需要大量的计算资源。因此，本文旨在研究如何在并行系统中求解Euler方程并提高并行性能。

设计/方法/方法

非连续Galerkin离散化用于可压缩的无粘性Euler方程。使用多级域分解策略来处理计算网格并确保计算负载平衡。总变差减小（TVD）Runge-Kutta（RK）方案与多网格策略结合使用，可进一步提高并行效率。此外，牛顿块高斯-赛德尔（GS）方法被用来加速收敛并提高迭代效率。

发现

针对M6机翼和DLR-F6构型，围绕NACA0012机翼周围的可压缩无粘性流动问题进行了数值实验。平行加速度接近线性收敛。结果表明，该并行算法可显着减少计算时间，合理分配内存，具有较高的并行效率和速度，非常适合多指令流，多数据流模型的大规模科学计算问题。

创意/价值

提出了并行的DGFEM与TVD RK和Newton Block GS方法相结合的方法，用于非结构化网格上的双曲守恒律。