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Parallel discontinuous Galerkin finite element method for computing hyperbolic conservation law on unstructured meshes

Zhijian Duan (School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, China; Department of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, China and Department of Mathematics and Information Science, Xianyang Normal University, Xianyang, China)
Gongnan Xie (Department of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 14 October 2020

Issue publication date: 3 May 2021

121

Abstract

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.

Keywords

Acknowledgements

This research was supported by the Aviation science foundation of China (No.: 2017ZA53001), the National Natural Science Research Program of China (No.: 6373174), the 13th five-year Research Program of Shaanxi Province of China (No.: SGH18H356).

Citation

Duan, Z. and Xie, G. (2021), "Parallel discontinuous Galerkin finite element method for computing hyperbolic conservation law on unstructured meshes", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 5, pp. 1410-1431. https://doi.org/10.1108/HFF-11-2019-0838

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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