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coiflet wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity

Advances in Applied Mathematics and Mechanics 2023年第3期15卷 684-718页

作者： Sohail Ahmed Hang Xu Qiang Sun State Key Lab of Ocean Engineering School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China Australian Research Council Centre of Excellence for Nanoscale BioPhotonics School of ScienceRMIT UniversityMelbourneVIC 3001Australia

In this paper,the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is *** Buongiorno model is applied to descirbe the nanofluid *** the top and bottom horizontal walls of the cavity are adiabatic,and there is a temperature difference between the left and right vertical *** non-dimensional governing equations are obtained when the stream-vorticity formulation of function is used,which are solved by the recently developed robust coiflet wavelet homotopy analysis method.A rigid verification for the solver is ***,the effects of various physics parameters including the Rayleigh number,the buoyancy ratio parameter,the bioconvection Rayleigh number,the Prandtl number,the Brownian motion parameter,the thermophoresis parameter,the heat generation parameter,the Lewis number,the bioconvection Peclet number and the Schmidt number on this complicated natural convection are *** is known that natural convection is closely related to our daily life owing to its wide existence in nature and engineering *** believe that our work will make a significant contribution to a better understanding of the natural convection of a complex fluid in a cavity with suspensions of both inorganic nanoparticles and organic microorganisms.

关键词： Cavity flow natural convection bio-thermal convection coiflet wavelet homotopy analysis method

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A Novel wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations

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Advances in Applied Mathematics and Mechanics 2023年第4期15卷 964-983页

作者： Yue Zhou Hang Xu State Key Lab of Ocean Engineering School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

The coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first *** Korteweg-de Vries(KdV)equation,the Burgers equation and the Korteweg-de Vries-Burgers(KdVB)equation are examined as illustrative *** and accuracy of the proposed method are assessed in terms of relative variance and the maximum error *** results are found in good agreement with exact solutions and numerical solutions reported in previous ***,it is found that the solution accuracy is closely related to the resolution level and the convergence-control *** is also found that our proposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear *** is expected that this approach can be further used to solve complicated unsteady problems in the fields of science and engineering.

关键词： coiflet wavelet homotopy analysis method wavelet-homotopy method wave equations unsteady

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A sixth-order wavelet integral collocation method for solving nonlinear boundary value problems in three dimensions

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Acta Mechanica Sinica 2022年第2期38卷 81-92,I0003页

作者： Zhichun Hou Jiong Weng Xiaojing Liu Youhe Zhou Jizeng Wang Key Laboratory of Mechanics on Disaster and Environment in Western China the Ministry of EducationLanzhou 730000China College of Civil Engineering and Mechanics Lanzhou UniversityLanzhou 730000China

A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three *** order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary *** applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation *** validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman *** demonstrate that the present method has higher accuracy and convergence rate than most existing numerical *** importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems.

关键词： Nonlinear boundary value problems Eighth-order derivative coiflet wavelet Integral collocation method Von Karman plate

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