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An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method
Pan, Xinglin1; Zhou, Yan1; Dong, Ping1; Shi, Huabin2
2022-04-06
Source PublicationEUROPEAN JOURNAL OF MECHANICS B-FLUIDS
ISSN0997-7546
Volume95Pages:94-105
Abstract

Meshless methods have become an essential numerical tool for simulating a wide range of flow–structure interaction problems. However, the way by which the impermeable solid boundary condition is implemented can significantly affect the accuracy of the results and computational cost. This paper develops an improved boundary scheme through a weak formulation for the boundary particles based on Pressure Poisson's Equation (PPE). In this scheme, the wall boundary particles simultaneously satisfy the PPE in the local integration domain by adopting the Meshless Local Petrov–Galerkin method with the Rankine source solution (MLPG_R) integration scheme (Ma, 2005b) and the Neumann boundary condition, i.e., normal pressure gradient condition, on the wall boundary which truncates the local integration domain. The new weak formulation vanishes the derivatives of the unknown pressure at wall particles and is discretized in the truncated support domain without extra artificial treatment. This improved boundary scheme is validated by analytical solutions, numerical benchmarks, and experimental data in the cases of patch tests, lid-driven cavity, flow over a cylinder and monochromic wave generation. Second-order convergent rate is achieved even for disordered particle distributions. The results show higher accuracy in pressure and velocity, especially near the boundary, compared to the existing boundary treatment methods that directly discretize the pressure Neumann boundary condition.

KeywordFlow Around Structures Meshless Local Petrov–galerkin Method Wall Boundary Conditions Weak Formulation
DOI10.1016/j.euromechflu.2022.03.014
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMechanics ; Physics
WOS SubjectMechanics ; Physics, Fluids & Plasmas
WOS IDWOS:000803794600005
PublisherELSEVIERRADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS
Scopus ID2-s2.0-85129508195
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Document TypeJournal article
CollectionFaculty of Science and Technology
THE STATE KEY LABORATORY OF INTERNET OF THINGS FOR SMART CITY (UNIVERSITY OF MACAU)
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
Corresponding AuthorZhou, Yan
Affiliation1.School of Engineering, University of Liverpool, Liverpool, UK, L69 3BX, United Kingdom
2.State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, Avenida da Universidade, Taipa, Macao, China
Recommended Citation
GB/T 7714
Pan, Xinglin,Zhou, Yan,Dong, Ping,et al. An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method[J]. EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2022, 95, 94-105.
APA Pan, Xinglin., Zhou, Yan., Dong, Ping., & Shi, Huabin (2022). An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method. EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 95, 94-105.
MLA Pan, Xinglin,et al."An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method".EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 95(2022):94-105.
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