南方科技大学知识苑(SUSTech KC): Uniformly high-order bound-preserving OEDG schemes for two-phase flows

题名	Uniformly high-order bound-preserving OEDG schemes for two-phase flows
作者	Yan, Ruifang1,2 ; Abgrall, Remi 3; Wu, Kailiang1,2
通讯作者	Wu, Kailiang
发表日期	2024-09-01
DOI	10.1142/S0218202524500544
发表期刊	MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 影响因子和分区
ISSN	0218-2025
EISSN	1793-6314
摘要	This paper proposes and rigorously analyzes novel high-order bound-preserving oscillation-eliminating discontinuous Galerkin (BP-OEDG) schemes with the Harten-Lax-van Leer (HLL) numerical flux for the Kapila five-equation two-phase flow model. The evolution equation for the volume fraction is formulated as a conservative advection equation with an additional non-conservative source term. Utilizing a technical splitting approach, we design a uniformly high-order discretization for this source term, incorporating an "upwind" discretization of the non-conservative product at cell interfaces based on the HLL wave speeds. This method inherently ensures the symmetry of the volume fractions, which is crucial for establishing the bound-preserving property. The positivity of partial densities and internal energy is rigorously proven using the geometric quasilinearization (GQL) approach, which transforms the nonlinear pressure positivity constraint into equivalent linear constraints. To suppress potential spurious oscillations, we incorporate a scale-invariant and linearity-invariant oscillation elimination (OE) procedure that damps the DG modal coefficients after each Runge-Kutta stage, as proposed in [M. Peng, Z. Sun and K. Wu, OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws, Math. Comput. (2024), https://doi.org/10.1090/mcom/3998 ]. This OE procedure, acting as a post-processing filter based on the jumps of the DG solution at cell interfaces, is easy to implement, maintains the Abgrall equilibrium condition around an isolated material interface, and preserves the high-order accuracy of the DG schemes. The effectiveness and robustness of the proposed high-order BP-OEDG schemes are demonstrated through several benchmark numerical experiments.
关键词	Kapila five-equation discontinuous Galerkin method bound-preserving damping technique geometric quasilinearization oscillation-eliminating (OE) filter
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一 ; 通讯
资助项目	Shenzhen Science and Technology Program[RCJC20221008092757098] ; National Natural Science Foundation of China[12171227] ; Postdoctoral Fellowship Program of CPSF[GZB20240293]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001320022500001
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/834330
专题	理学院_数学系南方科技大学
作者单位	1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 2.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen 518055, Peoples R China 3.Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
第一作者单位	数学系; 南方科技大学
通讯作者单位	数学系; 南方科技大学
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Yan, Ruifang,Abgrall, Remi,Wu, Kailiang. Uniformly high-order bound-preserving OEDG schemes for two-phase flows[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2024.
APA	Yan, Ruifang,Abgrall, Remi,&Wu, Kailiang.(2024).Uniformly high-order bound-preserving OEDG schemes for two-phase flows.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES.
MLA	Yan, Ruifang,et al."Uniformly high-order bound-preserving OEDG schemes for two-phase flows".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2024).