Pub Date : 2024-02-01DOI: 10.4208/aamm.oa-2023-0099
Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity
{"title":"Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations","authors":"Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou","doi":"10.4208/aamm.oa-2023-0099","DOIUrl":"https://doi.org/10.4208/aamm.oa-2023-0099","url":null,"abstract":"In this paper, we study the adaptive planewave discretization for a cluster\u0000of eigenvalues of second-order elliptic partial differential equations. We first design\u0000an a posteriori error estimator and prove both the upper and lower bounds. Based on\u0000the a posteriori error estimator, we propose an adaptive planewave method. We then\u0000prove that the adaptive planewave approximations have the linear convergence rate\u0000and quasi-optimal complexity","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-01DOI: 10.4208/aamm.oa-2023-0041
Haidong Yu,Xiaobo Quan,Haipeng Wei,Matevž Dular, Song Fu
Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in Rayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $psi_v$ and $psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base on physical quantities–the Blake critical radius $R_b$ and the average maximum growth radius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM in which we implemented the modified momentum interpolation (MMI) method to ensure that the calculated results are independent of time step size. Three validation cases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $psi_v$ and $psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities. Moreover, it is discussed the potentiality of NDCM that is generally applied on the cavitating flow possessing with dispersed bubbly cloud.
{"title":"Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations","authors":"Haidong Yu,Xiaobo Quan,Haipeng Wei,Matevž Dular, Song Fu","doi":"10.4208/aamm.oa-2023-0041","DOIUrl":"https://doi.org/10.4208/aamm.oa-2023-0041","url":null,"abstract":"Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in\u0000Rayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $psi_v$ and $psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base\u0000on physical quantities–the Blake critical radius $R_b$ and the average maximum growth\u0000radius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM\u0000in which we implemented the modified momentum interpolation (MMI) method to\u0000ensure that the calculated results are independent of time step size. Three validation\u0000cases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $psi_v$ and $psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities.\u0000Moreover, it is discussed the potentiality of NDCM that is generally applied on the\u0000cavitating flow possessing with dispersed bubbly cloud.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"30 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0278
Chunjie Zhang, Changxin Qiu, Xiaofang Zhou and Xiaoming He
{"title":"Cell-Average Based Neural Network Method for Hunter-Saxton Equations","authors":"Chunjie Zhang, Changxin Qiu, Xiaofang Zhou and Xiaoming He","doi":"10.4208/aamm.oa-2022-0278","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0278","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" 32","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139392140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0108
Yanli Chen, Tie Zhang and Ying Sheng
{"title":"A Primal-Dual Discontinuous Galerkin Finite Element Method for Ill-Posed Elliptic Cauchy Problems","authors":"Yanli Chen, Tie Zhang and Ying Sheng","doi":"10.4208/aamm.oa-2022-0108","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0108","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"361 17","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139394389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0275
Yang Wang, Liang Shi, Yong Liu
{"title":"A Buckley-Leverett Theory Based Lattice Boltzmann Method for Immiscible Two-Phase Flow with Viscous Coupling in Porous Media","authors":"Yang Wang, Liang Shi, Yong Liu","doi":"10.4208/aamm.oa-2022-0275","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0275","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139392980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0183
Lei Zhao, Wenqiang Zhou, Xinliang Li, Shaolong Zhang and Yongming Zhang
{"title":"Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones using the BiGlobal-$e^N$ Method","authors":"Lei Zhao, Wenqiang Zhou, Xinliang Li, Shaolong Zhang and Yongming Zhang","doi":"10.4208/aamm.oa-2022-0183","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0183","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"34 19","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139394963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2023-0107
Z. Yuan, Z. Chen, C. Shu, Y. Liu and Z. Zhang
{"title":"A Novel Construction of Distribution Function through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy","authors":"Z. Yuan, Z. Chen, C. Shu, Y. Liu and Z. Zhang","doi":"10.4208/aamm.oa-2023-0107","DOIUrl":"https://doi.org/10.4208/aamm.oa-2023-0107","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" 22","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139393125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0206
Zhixin Liu null, Minghui Song and Shicang Song
{"title":"An Isoparametric Finite Element Method for Reissner-Mindlin Plate Problem on Curved Domain","authors":"Zhixin Liu null, Minghui Song and Shicang Song","doi":"10.4208/aamm.oa-2022-0206","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0206","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"120 24","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139395957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01DOI: 10.4208/aamm.oa-2022-0127
Jun Lu, Lin Qiu, Yingjie Liang and Ji Lin
{"title":"Compressive Strength Prediction of High-Performance Hydraulic Concrete using a Novel Neural Network Based on the Memristor","authors":"Jun Lu, Lin Qiu, Yingjie Liang and Ji Lin","doi":"10.4208/aamm.oa-2022-0127","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0127","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"10 s2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139394758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.4208/aamm.oa-2023-0046
Congying Li, Liang Tang and Jie Zhou
{"title":"Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations","authors":"Congying Li, Liang Tang and Jie Zhou","doi":"10.4208/aamm.oa-2023-0046","DOIUrl":"https://doi.org/10.4208/aamm.oa-2023-0046","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"7 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139189599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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