Generalized analytical solutions to sequentially coupled multi-species advective–dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

2012 ◽  
Vol 456-457 ◽  
pp. 101-109 ◽  
Author(s):  
Jui-Sheng Chen ◽  
Chen-Wuing Liu ◽  
Ching-Ping Liang ◽  
Keng-Hsin Lai
Keyword(s):  
Boundary Condition ◽  
Analytical Solutions ◽  
Transport Equations ◽  
Time Dependent ◽  
Finite Domain ◽  
Dispersive Transport ◽  
Arbitrary Time

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 Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

2011 ◽  
Vol 8 (2) ◽  
pp. 4099-4120
Author(s):  
J.-S. Chen ◽  
C.-W. Liu
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Concentration Field ◽  
Generalized Solution ◽  
Spatial Domain ◽  
Time Dependent ◽  
Hydrodynamic Dispersion ◽  
Arbitrary Time ◽  
Special Cases ◽  
Inlet Boundary Condition

Abstract. This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

scholarly journals Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

2011 ◽  
Vol 15 (8) ◽  
pp. 2471-2479 ◽  
Author(s):  
J.-S. Chen ◽  
C.-W. Liu
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Generalized Solution ◽  
Spatial Domain ◽  
Time Dependent ◽  
Hydrodynamic Dispersion ◽  
Arbitrary Time ◽  
Special Cases ◽  
Inlet Boundary Condition

Abstract. This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption, and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Some special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement between the analytical and numerical solutions. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

scholarly journals Analytical solutions for linearized Richards Equation with arbitrary time-dependent surface fluxes

2001 ◽  
Vol 37 (4) ◽  
pp. 1091-1093 ◽  
Author(s):  
Jiann-Mou Chen ◽  
Yih-Chi Tan ◽  
Chu-Hui Chen ◽  
J.-Y. Parlange
Keyword(s):  
Analytical Solutions ◽  
Surface Fluxes ◽  
Time Dependent ◽  
Richards Equation ◽  
Arbitrary Time

An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Wave Motion ◽  
2014 ◽  
Vol 51 (1) ◽  
pp. 168-192 ◽  
Author(s):  
Silvia Falletta ◽  
Giovanni Monegato
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Time Dependent
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