A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing

doi:10.1016/j.jcp.2024.113459

	A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing
	Huang, Haohan 1; Li XL(李新亮)2 ; Fu, Lin 1,3,4,5
通讯作者	Fu, Lin([email protected])
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
	2025
卷号	520 页码:20
ISSN	0021-9991
摘要	In recent years, Runge-Kutta Discontinuous Galerkin (RKDG) methods have gained substantial attention in solving hyperbolic conservation laws, attributed to their high-order accuracy and adaptability to unstructured meshes. However, standard RKDG methods cannot capture discontinuities without oscillation unless they are supplemented with troubled cell indicators and limiters. Existing indicators, such as the total variation bounded (TVB) minmod indicator and the KXRCF indicator, typically depend on a critical parameter tied to the equation's solution, necessitating tuning for different cases. In terms of limiters, the popular limiters even fail to guarantee the high-order property in the smooth regions. The advent of Weighted Essentially Non-Oscillatory (WENO) schemes prompts the implementation of WENO limiters for RKDG methods, preserving high-order properties. However, WENO-family schemes exhibit significant numerical dissipation, potentially smearing small-scale flow structures. In this work, the Targeted Essentially Non-Oscillatory (TENO) indicator [1] is utilized, which leverages the nonlinear weighting strategy of the TENO scheme to separate high-wavenumber physical fluctuations and genuine discontinuities from smooth regions with a unified set of parameters. For troubled cells, a novel limiter is proposed for structured meshes, which combines a TENO scheme for resolving high-wavenumber physical fluctuations and a novel non-polynomial Tangent of Hyperbola for the INterface Capturing (THINC) scheme for resolving genuine discontinuities with extremely low numerical dissipation. Furthermore, the shifting between the TENO and THINC schemes is based on a new boundary variation diminishing (BVD) strategy, which only relies on compact neighborhoods and is significantly simpler than its predecessors. Meanwhile, a new strategy is proposed to ensure the consistency of the new limiter applied for 1D and 2D cases. A set of 1D and 2D benchmark cases including strong shockwaves and a broad range of flow length scales is simulated with uniform meshes for 1D cases and structured quadrilateral meshes for 2D cases to demonstrate the performance of the new numerical scheme. The indicator does not activate any limiters in the accuracy test cases to ensure the high-order property of the whole numerical
关键词	PDEs Runge-Kutta discontinuous Galerkin methods TENO WENO Hyperbolic conservation laws
DOI	10.1016/j.jcp.2024.113459
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:001331109500001
关键词[WOS]	DISCONTINUOUS GALERKIN METHOD ; FINITE-ELEMENT-METHOD ; TARGETED ENO SCHEMES ; HERMITE WENO SCHEMES ; CONSERVATION-LAWS ; VOLUME METHOD ; EFFICIENT IMPLEMENTATION ; LIMITERS ; FLOW ; SIMULATIONS
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
资助项目	National Key R&D Program of China[2022YFA1004500] ; State Key Laboratory of High-Temperature Gas Dynamics[2023KF25] ; National Natural Science Foundation of China[12422210] ; Research Grants Council (RGC) of the Government of Hong Kong Special Administrative Region (HKSAR) ; RGC/ECS Project[26200222] ; RGC/GRF Project[16201023] ; RGC/STG Project[STG2/E-605/23-N] ; Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone[HZQB-KCZYB-2020083]
项目资助者	National Key R&D Program of China ; State Key Laboratory of High-Temperature Gas Dynamics ; National Natural Science Foundation of China ; Research Grants Council (RGC) of the Government of Hong Kong Special Administrative Region (HKSAR) ; RGC/ECS Project ; RGC/GRF Project ; RGC/STG Project ; Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone
论文分区	一类/力学重要期刊
力学所作者排名	2
RpAuthor	Fu, Lin
引用统计
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/96976
专题	高温气体动力学国家重点实验室
作者单位	1.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China; 2.Chinese Acad Sci, Inst Mech, LHD, Beijing 100190, Peoples R China; 3.Hong Kong Univ Sci & Technol, Dept Mech & Aerosp Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China; 4.HKUST Shenzhen Hong Kong Collaborat Innovat Res In, Shenzhen, Peoples R China; 5.Hong Kong Univ Sci & Technol, Shenzhen Res Inst, Shenzhen, Peoples R China
推荐引用方式 GB/T 7714	Huang, Haohan,Li XL,Fu, Lin. A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2025,520:20.Rp_Au:Fu, Lin
APA	Huang, Haohan,李新亮,&Fu, Lin.(2025).A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing.JOURNAL OF COMPUTATIONAL PHYSICS,520,20.
MLA	Huang, Haohan,et al."A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing".JOURNAL OF COMPUTATIONAL PHYSICS 520(2025):20.