Pub Date : 2023-04-01DOI: 10.4208/aamm.oa-2022-0022
Adyllyson H. Nascimento and Eugênio S. Rosa
{"title":"A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows","authors":"Adyllyson H. Nascimento and Eugênio S. Rosa","doi":"10.4208/aamm.oa-2022-0022","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0022","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43187173","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 : 2023-04-01DOI: 10.4208/aamm.oa-2022-0019
. A Nitsche-based element-free Galerkin (EFG) method for solving semilinear elliptic problems is developed and analyzed in this paper. The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function. A simple iterative scheme is used to deal with the nonlinear integral term. We proved the existence, uniqueness and convergence of the weak solu-tion sequence for continuous level of the simple iterative scheme. A commonly used assumption for approximate space, sometimes called inverse assumption, is proved. Optimal order error estimates in L 2 and H 1 norms are proved for the linear and semi-linear elliptic problems. In the actual numerical calculation, the characteristic distance h does not appear explicitly in the parameter β introduced by the Nitsche method. The theoretical results are confirmed numerically.
{"title":"A Nitsche-Based Element-Free Galerkin Method for Semilinear Elliptic Problems","authors":"","doi":"10.4208/aamm.oa-2022-0019","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0019","url":null,"abstract":". A Nitsche-based element-free Galerkin (EFG) method for solving semilinear elliptic problems is developed and analyzed in this paper. The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function. A simple iterative scheme is used to deal with the nonlinear integral term. We proved the existence, uniqueness and convergence of the weak solu-tion sequence for continuous level of the simple iterative scheme. A commonly used assumption for approximate space, sometimes called inverse assumption, is proved. Optimal order error estimates in L 2 and H 1 norms are proved for the linear and semi-linear elliptic problems. In the actual numerical calculation, the characteristic distance h does not appear explicitly in the parameter β introduced by the Nitsche method. The theoretical results are confirmed numerically.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41687009","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}
In the hybrid RANS-LES simulations, proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible. Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model, which is important for the recovery process. The approximation of the length scale for the Spalart-Allmaras (S-A) model is not a trivial issue since the model's one-equation nature. As a direct analogy, the approximations could be obtained from the definition of the Prandtl's mixing length. Moreover, this paper proposes a new algebraic expression to approximate the intrinsic length scale of the S-A model. The underlying transportation mechanism of S-A model are largely exploited in the derivation of this new expression. The new proposed expression is employed in the generation of synthetic turbulence to perform the hybrid RANS-LES simulation of canonical wall-bounded turbulent flows. The comparisons demonstrated the feasibility and improved performance of the new length scale on generating synthetic turbulence at the LES inlet.
{"title":"On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model","authors":"Qilong Guo, Pengxin Liu, Chen Li, Dong Sun, Xianxu Yuan","doi":"10.4208/aamm.oa-2021-0298","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0298","url":null,"abstract":"In the hybrid RANS-LES simulations, proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible. Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model, which is important for the recovery process. The approximation of the length scale for the Spalart-Allmaras (S-A) model is not a trivial issue since the model's one-equation nature. As a direct analogy, the approximations could be obtained from the definition of the Prandtl's mixing length. Moreover, this paper proposes a new algebraic expression to approximate the intrinsic length scale of the S-A model. The underlying transportation mechanism of S-A model are largely exploited in the derivation of this new expression. The new proposed expression is employed in the generation of synthetic turbulence to perform the hybrid RANS-LES simulation of canonical wall-bounded turbulent flows. The comparisons demonstrated the feasibility and improved performance of the new length scale on generating synthetic turbulence at the LES inlet.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47836589","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 : 2023-03-01DOI: 10.4208/aamm.oa-2022-0176
A. Mohammadpour, S. J. Mehrabadi, P. Monfared
{"title":"Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory","authors":"A. Mohammadpour, S. J. Mehrabadi, P. Monfared","doi":"10.4208/aamm.oa-2022-0176","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0176","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46801517","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 : 2023-03-01DOI: 10.4208/aamm.oa-2022-0173
Jiaqi Zhang, Y. Zhou
{"title":"Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian","authors":"Jiaqi Zhang, Y. Zhou","doi":"10.4208/aamm.oa-2022-0173","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0173","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44167898","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 : 2023-02-01DOI: 10.4208/aamm.oa-2022-0195
Z. Yuan, Z. Chen, C. Shu, Y. Zhang
{"title":"Construction of Non-Equilibrium Gas Distribution Functions through Expansions in Peculiar Velocity Space","authors":"Z. Yuan, Z. Chen, C. Shu, Y. Zhang","doi":"10.4208/aamm.oa-2022-0195","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0195","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43595351","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 : 2023-02-01DOI: 10.4208/aamm.oa-2022-0214
Q-B Yu, Shuaimin Wang, Junfeng Xu
{"title":"A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints","authors":"Q-B Yu, Shuaimin Wang, Junfeng Xu","doi":"10.4208/aamm.oa-2022-0214","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0214","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49639866","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 : 2023-02-01DOI: 10.4208/aamm.oa-2022-0003
Mengyue Wu, Jianhua Zhang
{"title":"A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design","authors":"Mengyue Wu, Jianhua Zhang","doi":"10.4208/aamm.oa-2022-0003","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0003","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43041691","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 : 2023-02-01DOI: 10.4208/aamm.oa-2021-0270
J. Yue, Yu Wang, Yan Li
{"title":"A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems","authors":"J. Yue, Yu Wang, Yan Li","doi":"10.4208/aamm.oa-2021-0270","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0270","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47125060","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 : 2023-02-01DOI: 10.4208/aamm.oa-2022-0068
Huiling Chen, Chunmei Zhang, Yu Xu
{"title":"Partial Topology Identification of Stochastic Multi-Weighted Complex Networks Based on Graph-Theoretic Method and Adaptive Synchronization","authors":"Huiling Chen, Chunmei Zhang, Yu Xu","doi":"10.4208/aamm.oa-2022-0068","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0068","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49264778","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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