Exact analytical solutions for three-dimensional multispecies advective-dispersive transport equations sequentially coupled with first-order decay reactions in a semi-infinite domain

2020 ◽  
Author(s):  
Zhong-Yi Liao ◽  
Jui-Sheng Chen
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Chlorinated Solvents ◽  
Transport Equations ◽  
Finite Domain ◽  
Dispersive Transport ◽  
Exact Analytical Solutions ◽  
First Order

<p>Analytical solutions to a set of simultaneous multispecies advective-dispersive transport equations sequentially coupled with first-order decay reactions have been widely used to describe the movements of decaying or degradable contaminants such as chlorinated solvents, nitrogens and pesticides in the subsurface. This study presents an exact analytical solutions for three-dimensional coupled multispecies transport in a semi-finite domain. The analytical model are derived for both the first-type and third-type inlet boundary conditions. A method of consecutive applications of three integral transformation techniques in combination with sequential substitutions is adopted to derive the analytical solutions to the governing equation system. The developed analytical model is robustly verified with a chlorinated solvent transport problem. It is applied to investigate the effect of inlet-boundary conditions on the multispecies plume migration and the model could be a very efficient tool that can be used to simulate the degradable contaminant sites.</p><p>請在此處插入您的抽象HTML。</p>

scholarly journals Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nemat Dalir
Keyword(s):  
Fluid Mechanics ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Second Order ◽  
Nonlinear Pdes ◽  
Initial Value ◽  
Exact Analytical Solutions ◽  
First Order

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

Refined First-Order Shear Deformation Theory Models for Composite Laminates

2003 ◽  
Vol 70 (3) ◽  
pp. 381-390 ◽  
Author(s):  
F. Auricchio ◽  
E. Sacco
Keyword(s):  
Shear Deformation ◽  
Analytical Solutions ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Quadratic Functions ◽  
Shear Stresses ◽  
Stress Profile ◽  
First Order ◽  
Out Of Plane

In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stresses can be derived without post-processing procedures. Some numerical applications are presented in order to verify the effectiveness of the proposed formulations. In particular, analytical solutions obtained using the developed models are compared with the exact three-dimensional solution, with other classical laminate analytical solutions and with finite element results. Finally, we note that the proposed formulations may represent a rational base for the development of effective finite elements for composite laminates.

Two and Three-Dimensional Flow using Finite Elements

1969 ◽  
Vol 73 (707) ◽  
pp. 961-964 ◽  
Author(s):  
J. H. Argyris ◽  
G. Mareczek ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Boundary Conditions ◽  
Stream Function ◽  
Three Dimensional ◽  
Finite Domain ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Triangular Elements ◽  
Compressibility Effects

The method of finite elements is in certain cases advantageous when dealing with flow problems in a finite domain. This is particularly so when attempting to include subcritical compressibility effects. In the present note we first consider the two-dimensional flow using TRIC and TRIM-like triangular elements in conjunction with the concept of the stream function, which is assigned to the nodal points of the elements. The application of the stream function allows a direct and exact satisfaction of the boundary conditions. Strictly the elements in question could also be used in conjunction with the potential function but the observance of the boundary conditions is then cumbersome.

scholarly journals First Order Framework for Gauge k-Vortices

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
D. Bazeia ◽  
L. Losano ◽  
M. A. Marques ◽  
R. Menezes
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Boundary Conditions ◽  
Unit Circle ◽  
Analytical Solutions ◽  
Covariant Derivative ◽  
Lagrangian Density ◽  
Kinetic Term ◽  
First Order

We study vortices in generalized Maxwell-Higgs models, with the inclusion of a quadratic kinetic term with the covariant derivative of the scalar field in the Lagrangian density. We discuss the stressless condition and show that the presence of analytical solutions helps us to define the model compatible with the existence of first order equations. A method to decouple the first order equations and to construct the model is then introduced and, as a bonus, we get the energy depending exclusively on a function of the fields calculated from the boundary conditions. We investigate some specific possibilities and find, in particular, a compact vortex configuration in which the energy density is all concentrated in a unit circle.

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