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Dynamics of some more invariant solutions of (3 + 1)-Burgers system (3 + 1)-Burgers系统若干更不变量解的动力学
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916693
R. Kumar, M. Kumar, A. Tiwari
{"title":"Dynamics of some more invariant solutions of (3 + 1)-Burgers system","authors":"R. Kumar, M. Kumar, A. Tiwari","doi":"10.1080/15502287.2021.1916693","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916693","url":null,"abstract":"Abstract This paper is an application of the similarity transformations method via Lie-group theory. This method is applied to the (3 + 1)-dimensional Burgers system to derive its invariant solutions. The Burgers system has many physical applications in fluid mechanics, heat conduction, plasma physics, traffic flows, and in some others like acoustic transmission and structure of shock waves. Since Burgers system consists of a system of nonlinear partial differential equations (PDEs), and therefore, it is a difficult task to obtain its exact solution. A system of PDEs is reduced into a system of ODEs and finally solved by making appropriate assumptions and choice of arbitrary functions and constants appeared therein. Hence, the obtained exact solutions compromised multisolitons, kink waves, periodic multisolitons, elastic mutisolitons and stationary waves.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128225806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Effect of mass transfer and radiation on mixed convection boundary layer flow over a permeable vertical cylinder with surface heat flux and mass flux 传质和辐射对具有表面热通量和质量通量的可透垂直圆柱体混合对流边界层流动的影响
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916692
N. Joshi, V. Bisht, A. Bhakuni, G. Pathak
{"title":"Effect of mass transfer and radiation on mixed convection boundary layer flow over a permeable vertical cylinder with surface heat flux and mass flux","authors":"N. Joshi, V. Bisht, A. Bhakuni, G. Pathak","doi":"10.1080/15502287.2021.1916692","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916692","url":null,"abstract":"Abstract In this study, the effects of mass transfer and radiation on mixed convection boundary layer flow over a permeable vertical cylinder with surface heat flux and mass flux have been investigated. The free stream velocity and the surface heat flux are assumed to vary linearly with the distance from the leading edge. The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically for both assisting and opposing flow regimes using a fourth-order Runge-Kutta scheme with the shooting method. Velocity, temperature, and concentration distributions were numerically discussed and presented in the graphs. Skin-friction coefficient, Nusselt number, and Sherwood number on the cylinder were derived and discussed numerically. Their numerical values for various values of physical parameters were presented in the tables. The results obtained are comparing with the published results for various authors, and it is found to be a good agreement.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130543094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Computational and mathematical approach for recent problems in mathematical sciences 数学科学中最新问题的计算和数学方法
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916172
M. Ram, Vijay Kumar, G. S. Ladde
{"title":"Computational and mathematical approach for recent problems in mathematical sciences","authors":"M. Ram, Vijay Kumar, G. S. Ladde","doi":"10.1080/15502287.2021.1916172","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916172","url":null,"abstract":"This special issue on Computational and mathematical approach for recent problems in mathematical sciencesis the compilation of the short listed papers of 4th International Conference on Mathematical Techniques in Engineering Applications (ICMTEA2020) held during 4–5 December 2020 in Graphic Era (Deemed to be University), Dehradun, Uttarakhand, India. In this issue, we selected nine papers which have gone through several rounds of review and revision, and represent a cross-section of research in mathematical analysis and computational approach of solving complex mathematical problems occurs in engineering and sciences that touch upon both technical and managerial issues. The articles on mathematical analysis, computational approach, efficient algorithm for computation, solving nonlinear reaction-diffusion equation, effect of mass transfer and radiation on mixed convection boundary layer flow, solutions of (3þ 1)-burgers system, optimization using NSGA-II, numerical treatment for the comparative study of MHD flow of Nano liquids, and computational study of seismic wave propagation. The guest editors are grateful to contributors who have made remarkable contributions and present their papers in the ICMTEA2020 during COVID19 pandemic. The guest editors are also grateful to reviewers for their valuable comments and suggestions which helped in improving the quality of the papers. Guest editors are also highly thankful to Editor-in-Chief & Associate Editors for providing the continuous support and constructive suggestions during the review process and shaping the special issue. We hope that this special issue makes significant contributions in the field of recent advancement in mathematical and computational field. We acknowledge International Journal for Computational Methods in Engineering Science & Mechanics for their kind support and help in bringing out this special issue.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121629766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical analysis of MHD stagnation point flow of Cu-blood nanofluid past an exponential stretchable surface 铜血纳米流体通过指数可拉伸表面的MHD滞止点流动的数学分析
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916173
Santosh Chaudhary, Ajay V. Singh, K. Kanika
{"title":"Mathematical analysis of MHD stagnation point flow of Cu-blood nanofluid past an exponential stretchable surface","authors":"Santosh Chaudhary, Ajay V. Singh, K. Kanika","doi":"10.1080/15502287.2021.1916173","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916173","url":null,"abstract":"Abstract Two dimensional, steady, incompressible magnetohydrodynamic flow near a stagnation region toward an exponentially stretching plate is numerically investigated in present illustration. Base fluid– blood, along with copper (Cu) is taken to compose the nanofluid and different shapes of nanoparticles such as sphere, hexahedron, tetrahedron, column and lamina are taken into considerations. By using the suitable similarity transformations, the consequent equations are converted to a set of nonlinear ordinary differential equations. The spectral relaxation method is applied to compute the solution of the system. Several parameters like stretching parameter, nanoparticle volume fraction, magnetic parameter, Brinkman number and empirical shape factor are emerging in the governing equations, which affects the fluid flow veocity and temperature. These changes are given in the graphical form. Furthermore, impacts of specified parameters on surface shear stress and surface heat flux are also enlisted in form of tables. To ensure the validation of the results, the present results are compared with already existing data.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"63 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132738276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A numerical regime for 1-D Burgers’ equation using UAT tension B-spline differential quadrature method 用UAT张力b样条微分求积分法求一维Burgers方程的数值形式
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916175
Mamta Kapoor, V. Joshi
{"title":"A numerical regime for 1-D Burgers’ equation using UAT tension B-spline differential quadrature method","authors":"Mamta Kapoor, V. Joshi","doi":"10.1080/15502287.2021.1916175","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916175","url":null,"abstract":"Abstract Present work deals with the numerical solution of 1D nonlinear Burgers’ equation. In this article, modified cubic uniform algebraic trigonometric tension B-spline is implemented as the basis function. Modified cubic UAT tension B-spline is incorporated in the differential quadrature method to fetch the values of weighting coefficients, as finding the weighting coefficients is the main key in differential quadrature method. After the spatial discretization of the equations, the reduced system of ordinary differential equations is obtained, which is tackled by employing the SSP-RK43 scheme. Accuracy of the present regime is verified by implementing notion of and error norms. On making comparisons with the earlier outcomes, it is noticed that present regime has produced better results, as well as is easy to implement. Main outcome of this work lies in findings of the better numerical approximations of some linear and nonlinear partial differential equations, specifically where the analytical solutions do not exist.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130199965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Jacobi Collocation Technique to Solve Nonlinear Reaction-Diffusion Equation 求解非线性反应扩散方程的Jacobi配置技术
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916691
Shubham Jaiswal, S. Das, R. Dubey, A. Tiwari
{"title":"Jacobi Collocation Technique to Solve Nonlinear Reaction-Diffusion Equation","authors":"Shubham Jaiswal, S. Das, R. Dubey, A. Tiwari","doi":"10.1080/15502287.2021.1916691","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916691","url":null,"abstract":"Abstract To analyze the transport phenomena in porous structure, one basically gets nonlinear reaction-diffusion equation. In this article, we have proposed a numerical technique to solve such problems using Legendre collocation technique. In the proposed scheme, Legendre polynomial are used along with operational matrices and spectral collocation method to convert the considered problems in systems of nonlinear algebraic equations that can be solved using Newton-Iteration method. The salient feature of the article is the exhibition of sub-diffusion nature of solution profile for different particular cases in the presence or absence of the source/sink term. The accuracy of the proposed method is exhibited through applying it to two existing problems having exact solutions and compared the results through error analysis which shows the efficiency and high accuracy of the approach.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114393120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A metaheuristic approach for the comparative study of MHD flow of nano liquids in a semi-porous channel 半多孔通道中纳米液体MHD流动比较研究的元启发式方法
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916700
Z. Uddin, R. Asthana, M. Awasthi, H. Hassan
{"title":"A metaheuristic approach for the comparative study of MHD flow of nano liquids in a semi-porous channel","authors":"Z. Uddin, R. Asthana, M. Awasthi, H. Hassan","doi":"10.1080/15502287.2021.1916700","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916700","url":null,"abstract":"Abstract In this paper, magneto-hydrodynamic flow of four different nanoliquids is presented. Two types of nanoparticles, viz. alumina and CuO are considered in water and ethylene glycol as base fluids. Appropriate models for nanoliquid physical properties are considered to incorporate the nanoparticle aggregation effects, nanoparticle shape, and size of the nanoparticles. Similarity transformations are used to convert the partial differential equations of the flow to nonlinear ordinary differential equations. The resultant system of equations is solved by Runge–Kutta finite difference method and an error function is designed which is optimized by using a metaheuristic algorithm, namely particle swarm optimization. The effect of flow parameters, viz. mass transfer parameter and Hartmann number and the nanoliquid parameters like nature of the base liquid, nanoparticle material, nanoparticle size, concentration of nanoparticle in base liquid on velocity distributions have been analyzed and discussed. The nanoparticle concentration and the particle size are found to have a significant role in the nanoliquid flow in the channel. The numerical results obtained from the proposed numerical method are validated with the previously published work under some special cases. The proposed numerical method holds excellent potential in mathematical modeling problems where the resultant equations are nonlinear coupled ordinary differential equations with unknown initial or boundary conditions.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129184838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Computational study of seismic wave propagation through metamaterial foundation 地震波通过超材料地基的计算研究
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916217
Aman Thakur, Arpan Gupta
{"title":"Computational study of seismic wave propagation through metamaterial foundation","authors":"Aman Thakur, Arpan Gupta","doi":"10.1080/15502287.2021.1916217","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916217","url":null,"abstract":"Abstract The present work is about metamaterial-based foundation design for attenuating seismic wave propagation. Metamaterials are artificially designed structures engineered for novel properties. These artificially designed structures can exhibit properties, which can be contra-intuitive and sometimes not available in nature. These metamaterials have frequency regions (called as bandgaps) for which significant attenuation of – P-waves and S-waves takes place. In this work, bandgaps have been computed using the finite element method and compared with the literature. Further, harmonic excitation is provided, and the frequency response function through the metamaterial region has been evaluated for various layers of the structure. The results show high S- and P-wave attenuation in the bandgap region, which can be engineered by designing the unit cell.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128642965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Multi-objective power distribution optimization using NSGA-II 基于NSGA-II的多目标功率分配优化
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-16 DOI: 10.1080/15502287.2021.1916696
K. Jain, Shashank Gupta, Divya Kumar
{"title":"Multi-objective power distribution optimization using NSGA-II","authors":"K. Jain, Shashank Gupta, Divya Kumar","doi":"10.1080/15502287.2021.1916696","DOIUrl":"https://doi.org/10.1080/15502287.2021.1916696","url":null,"abstract":"Abstract Power distribution is one of the major areas of electrical engineering. The issue of optimized power distribution is of great concern and here it is dealt with as a single- and multi-objective problem. We know that evolutionary algorithms have better efficiency in solving such problems. In this paper, we have applied heuristics non-dominated sorting genetic algorithm II (NSGA-II, multiple objective optimization algorithm) to optimize functions such as corona loss, efficiency, potential drop, resistive loss, and volume of the conductor. The NSGA-II has outperformed other algorithms involving the optimal solution. NSGA-II is not only simple in terms of programming but also achieves the desired high-quality optimal solutions in fewer iterations. After our experiment, we have optimized the various functions presented in this paper.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128239923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Semi-infinite crack between two dissimilar orthotropic strips 两个不同正交各向异性条之间的半无限裂缝
International Journal for Computational Methods in Engineering Science and Mechanics Pub Date : 2021-06-07 DOI: 10.1080/15502287.2021.1933262
P. Basak, S. Naskar, S. Mandal
{"title":"Semi-infinite crack between two dissimilar orthotropic strips","authors":"P. Basak, S. Naskar, S. Mandal","doi":"10.1080/15502287.2021.1933262","DOIUrl":"https://doi.org/10.1080/15502287.2021.1933262","url":null,"abstract":"Abstract The problem of a semi-infinite crack between two dissimilar orthotropic strips has been solved. Using the Fourier transform technique the problem has been converted to a standard Wiener-Hopf equation which has been solved for asymptotic cases only to deduce the expressions for the stress intensity factor and crack opening displacement. Finally the values of the stress intensity factor and crack opening displacement have been plotted graphically to show the effects of strip width and material orthotropy.","PeriodicalId":315058,"journal":{"name":"International Journal for Computational Methods in Engineering Science and Mechanics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125815698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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