Open Access

ARTICLE

High-Order DG Schemes with Subcell Limiting Strategies for Simulations of Shocks, Vortices and Sound Waves in Materials Science Problems

Zhenhua Jiang^1,*, Xi Deng^2,3, Xin Zhang¹, Chao Yan¹, Feng Xiao⁴, Jian Yu¹

1 College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
2 Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK
3 Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK
4 Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo, 152-8550, Japan

* Corresponding Author: Zhenhua Jiang. Email:

(This article belongs to the Special Issue: Recent Advances in Computational Fluid Dynamics)

Fluid Dynamics & Materials Processing 2024, 20(10), 2183-2204. https://doi.org/10.32604/fdmp.2024.053231

Received 18 April 2024; Accepted 20 August 2024; Issue published 23 September 2024

Abstract

Shock waves, characterized by abrupt changes in pressure, temperature, and density, play a significant role in various materials science processes involving fluids. These high-energy phenomena are utilized across multiple fields and applications to achieve unique material properties and facilitate advanced manufacturing techniques. Accurate simulations of these phenomena require numerical schemes that can represent shock waves without spurious oscillations and simultaneously capture acoustic waves for a wide range of wavelength scales. This work suggests a high-order discontinuous Galerkin (DG) method with a finite volume (FV) subcell limiting strategies to achieve better subcell resolution and lower numerical diffusion properties. By switching to the FV discretization on an embedded sub-cell grid, the method displays advantages with respect to both DG accuracy and FV shock-capturing ability. The FV scheme utilizes a class of high-fidelity schemes that are built upon the boundary variation diminishing (BVD) reconstruction paradigm. The method is therefore able to resolve discontinuities and multi-scale structures on the subcell level, while preserving the favorable properties of the high-order DG scheme. We have tested the present DG method up to the 6th-order accuracy for both smooth and discontinuous noise problems.

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Keywords

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