Pub Date : 2023-09-01DOI: 10.4208/aamm.oa-2021-0373
M. Salah, O. Civalek, O. Ragb
. In this study, a ( 3 + 1 ) dimensional unstable gas flow system is applied and solved successfully via differential quadrature techniques based on various shape functions. The governing system of nonlinear four-dimensional unsteady Navier–Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, Runge-Kutta 4th order method is employed to solve the resulting system of equations. To obtain the solution of this equation, a MATLAB code is designed. The validity of these techniques is achieved by the comparison with the exact solution where the error reach to ≤ 1 × 10 − 5 . Also, these solutions are discussed by seven various statistical analysis. Then, a parametric analysis is presented to discuss the effect of adiabatic index parameter on the velocity, pressure, and density profiles. From these computations, it is found that Discrete singular convolution based on Regularized Shannon kernels is a stable, efficient numerical technique and its strength has been appeared in this application. Also, this technique can be able to solve higher dimensional nonlinear problems in various regions of physical and numerical sciences.
{"title":"Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method","authors":"M. Salah, O. Civalek, O. Ragb","doi":"10.4208/aamm.oa-2021-0373","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0373","url":null,"abstract":". In this study, a ( 3 + 1 ) dimensional unstable gas flow system is applied and solved successfully via differential quadrature techniques based on various shape functions. The governing system of nonlinear four-dimensional unsteady Navier–Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, Runge-Kutta 4th order method is employed to solve the resulting system of equations. To obtain the solution of this equation, a MATLAB code is designed. The validity of these techniques is achieved by the comparison with the exact solution where the error reach to ≤ 1 × 10 − 5 . Also, these solutions are discussed by seven various statistical analysis. Then, a parametric analysis is presented to discuss the effect of adiabatic index parameter on the velocity, pressure, and density profiles. From these computations, it is found that Discrete singular convolution based on Regularized Shannon kernels is a stable, efficient numerical technique and its strength has been appeared in this application. Also, this technique can be able to solve higher dimensional nonlinear problems in various regions of physical and numerical sciences.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46928612","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 : 2023-09-01DOI: 10.4208/aamm.oa-2022-0184
Yan Zhang and Jun Zhu
{"title":"New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws","authors":"Yan Zhang and Jun Zhu","doi":"10.4208/aamm.oa-2022-0184","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0184","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48166990","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 : 2023-09-01DOI: 10.4208/aamm.oa-2022-0237
Rongfang Wu, Xiaoqin Shen, Dongyang Shi and Jiaping Yu
{"title":"Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model","authors":"Rongfang Wu, Xiaoqin Shen, Dongyang Shi and Jiaping Yu","doi":"10.4208/aamm.oa-2022-0237","DOIUrl":"https://doi.org/10.4208/aamm.oa-2022-0237","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48027733","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 : 2023-09-01DOI: 10.4208/aamm.oa-2021-0289
Do Quang Chan et al.
. In this article, the effects of temperature and size-dependent on the buckling behavior of functionally graded (FG) cylindrical nanopanels resting on elastic foundation using nonlocal strain gradient theory are investigated in detail analytical approach. According to a simple power-law distribution, the material properties of FG cylindrical nanopanels are assumed to vary continuously through the thickness direction. The Pasternak model is used to describe the reaction of the elastic foundation on the FG cylindrical nanopanels. The fundamental relations and stability equations are derived by applying the nonlocal strain gradient theory and the classical shell theory based on the adjacent equilibrium criterion. Using Galerkin’s method, the mechanical buckling behavior of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment is solved. The reliability of the obtained results has been veri-fied by comparison with the previous results in the literature. Based on the obtained results, the influences of the material length scale parameter, the nonlocal parameter, temperature increment, geometric parameters, material properties, and elastic foundation on buckling behaviors of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment are analyzed and discussed.
{"title":"An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak's Foundations in the Thermal Environment","authors":"Do Quang Chan et al.","doi":"10.4208/aamm.oa-2021-0289","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0289","url":null,"abstract":". In this article, the effects of temperature and size-dependent on the buckling behavior of functionally graded (FG) cylindrical nanopanels resting on elastic foundation using nonlocal strain gradient theory are investigated in detail analytical approach. According to a simple power-law distribution, the material properties of FG cylindrical nanopanels are assumed to vary continuously through the thickness direction. The Pasternak model is used to describe the reaction of the elastic foundation on the FG cylindrical nanopanels. The fundamental relations and stability equations are derived by applying the nonlocal strain gradient theory and the classical shell theory based on the adjacent equilibrium criterion. Using Galerkin’s method, the mechanical buckling behavior of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment is solved. The reliability of the obtained results has been veri-fied by comparison with the previous results in the literature. Based on the obtained results, the influences of the material length scale parameter, the nonlocal parameter, temperature increment, geometric parameters, material properties, and elastic foundation on buckling behaviors of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment are analyzed and discussed.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46630938","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 : 2023-08-01DOI: 10.4208/aamm.oa-2023-0059
H. Tian, Xianchu Yang, Chenguang Liu
. While the theory of peridynamics (PD) holds significant potential in engineering, its application is often limited by the significant computational costs by the nonlocality of PD. This research is based on a three-dimensional(3D) complex Tim-oshenko beam structure with six degrees of freedom. We propose a fast meshfree method based on the linear bond-based PD model of the stiffness matrix structure by ingeniously using the matrix decomposition strategy to maintain the Teoplitz structure of the stiffness matrix. This method significantly reduces the amount of calculation and storage without losing accuracy, reduces the amount of calculation from O ( N 2 ) to O ( N log N ) , and decreases the storage capacity from O ( N 2 ) to O ( N ) . We validate the effectiveness of our approach through numerical examples, particularly in multi-beam structures. We demonstrate that our method realizes algorithm acceleration in numerical simulations of multi-beam structures subjected to static concentrated loads.
{"title":"A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model","authors":"H. Tian, Xianchu Yang, Chenguang Liu","doi":"10.4208/aamm.oa-2023-0059","DOIUrl":"https://doi.org/10.4208/aamm.oa-2023-0059","url":null,"abstract":". While the theory of peridynamics (PD) holds significant potential in engineering, its application is often limited by the significant computational costs by the nonlocality of PD. This research is based on a three-dimensional(3D) complex Tim-oshenko beam structure with six degrees of freedom. We propose a fast meshfree method based on the linear bond-based PD model of the stiffness matrix structure by ingeniously using the matrix decomposition strategy to maintain the Teoplitz structure of the stiffness matrix. This method significantly reduces the amount of calculation and storage without losing accuracy, reduces the amount of calculation from O ( N 2 ) to O ( N log N ) , and decreases the storage capacity from O ( N 2 ) to O ( N ) . We validate the effectiveness of our approach through numerical examples, particularly in multi-beam structures. We demonstrate that our method realizes algorithm acceleration in numerical simulations of multi-beam structures subjected to static concentrated loads.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43053693","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 : 2023-06-01DOI: 10.4208/aamm.oa-2021-0352
W. Yin, Hongyu Qi null, P. Meng
{"title":"Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data","authors":"W. Yin, Hongyu Qi null, P. Meng","doi":"10.4208/aamm.oa-2021-0352","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0352","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42078055","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 : 2023-06-01DOI: 10.4208/aamm.oa-2020-0394
Amjad Ali, Zainab Bukhari, Hamayun Farooq null, Z. Abbas
{"title":"Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation","authors":"Amjad Ali, Zainab Bukhari, Hamayun Farooq null, Z. Abbas","doi":"10.4208/aamm.oa-2020-0394","DOIUrl":"https://doi.org/10.4208/aamm.oa-2020-0394","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47493329","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 : 2023-06-01DOI: 10.4208/aamm.oa-2021-0223
Yan Gu, Ji Lin null, C. Fan
{"title":"Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions","authors":"Yan Gu, Ji Lin null, C. Fan","doi":"10.4208/aamm.oa-2021-0223","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0223","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41969352","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 : 2023-06-01DOI: 10.4208/aamm.oa-2021-0280
Wang Kong, Zhenying Hong, Guangwei Yuan null, Z. Sheng
. In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.
{"title":"Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes","authors":"Wang Kong, Zhenying Hong, Guangwei Yuan null, Z. Sheng","doi":"10.4208/aamm.oa-2021-0280","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0280","url":null,"abstract":". In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70494914","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 : 2023-06-01DOI: 10.4208/aamm.oa-2021-0366
{"title":"A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field","authors":"","doi":"10.4208/aamm.oa-2021-0366","DOIUrl":"https://doi.org/10.4208/aamm.oa-2021-0366","url":null,"abstract":"","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44704070","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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