A hybrid Laplace transform finite analytic method for solving transport problems with large Peclet and Courant numbers

Wang, Wenke; Dai, Zhenxue; Li, Junting; Li-ling, Zhou

doi:10.1016/j.cageo.2012.05.020

Cited by 21 publications

(8 citation statements)

References 32 publications

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“… 27 , Wang et al . 28 , and Zhang et al . 29 for the saturated-unsaturated flow simulation was adopted in the validation.…”

Section: Discussionmentioning

confidence: 97%

“…The numerical simulation results computed from the saturated-unsaturated flow model 27 28 29 clearly show that, as long as the rate of drainage in the ditches exceeds the seepage capacity of the stream under a given streambed condition, the relationship between the stream and aquifer can be evolved from the hydraulic connection to disconnection ( Fig. 3 ).…”

Section: Discussionmentioning

confidence: 99%

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A quantitative analysis of hydraulic interaction processes in stream-aquifer systems

Wang

Dai

Zhao

et al. 2016

Sci Rep

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The hydraulic relationship between the stream and aquifer can be altered from hydraulic connection to disconnection when the pumping rate exceeds the maximum seepage flux of the streambed. This study proposes to quantitatively analyze the physical processes of stream-aquifer systems from connection to disconnection. A free water table equation is adopted to clarify under what conditions a stream starts to separate hydraulically from an aquifer. Both the theoretical analysis and laboratory tests have demonstrated that the hydraulic connectedness of the stream-aquifer system can reach a critical disconnection state when the horizontal hydraulic gradient at the free water surface is equal to zero and the vertical is equal to 1. A boundary-value problem for movement of the critical point of disconnection is established for an analytical solution of the inverted water table movement beneath the stream. The result indicates that the maximum distance or thickness of the inverted water table is equal to the water depth in the stream, and at a steady state of disconnection, the maximum hydraulic gradient at the streambed center is 2. This study helps us to understand the hydraulic phenomena of water flow near streams and accurately assess surface water and groundwater resources.

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“… 27 , Wang et al . 28 , and Zhang et al . 29 for the saturated-unsaturated flow simulation was adopted in the validation.…”

Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

A quantitative analysis of hydraulic interaction processes in stream-aquifer systems

Wang

Dai

Zhao

et al. 2016

Sci Rep

Self Cite

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“…The flow velocity used is u = 1 m per day and the dimensionless source concentration was C 0 = 10. Solute transport problems for D = 0.1, 2.5 and 10 m 2 per day were considered [17]. In the case of constant boundary condition (5), the concentrations at time t equal to 5, 10, 20, 30, 40, and 50 days are computed by EFDM and analytically (6).…”

Section: Methodsmentioning

confidence: 99%

Explicit finite difference solution for contaminant transport problems with constant and oscillating boundary conditions

Savovic

Djordjevich

2020

THERM SCI

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Original scientific paper https://doi.org/10.2298/TSCI190722422S For constant and oscillating boundary conditions, the 1-D advection-diffusion equation with constant coefficients, which describes a contaminant flow, is solved by the explicit finite difference method in a semi-infinite medium. It is shown how far the periodicity of the oscillating boundary carries on until diminishing to below appreciable levels a specified distance away, which depends on the oscillation characteristics of the source. Results are tested against an analytical solution reported for a special case. The explicit finite difference method is shown to be effective for solving the advection-diffusion equation with constant coefficients in semi-infinite media with constant and oscillating boundary conditions.

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“…As a methodology, the finite analytic method (FAM) was first introduced to mainly solve heat conduction and Navier-Strokes equations [20,21]. The combination, under FAM of the numerical method and analytical method, gives higher precision, good numerical stability, and fast convergence and is widely employed in fluid mechanics and groundwater dynamics [22][23][24][25].…”

Section: Shock and Vibrationmentioning

confidence: 99%

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

Cheng

Wang

Chen

et al. 2017

Shock and Vibration

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For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.

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A hybrid Laplace transform finite analytic method for solving transport problems with large Peclet and Courant numbers

Cited by 21 publications

References 32 publications

A quantitative analysis of hydraulic interaction processes in stream-aquifer systems

A quantitative analysis of hydraulic interaction processes in stream-aquifer systems

Explicit finite difference solution for contaminant transport problems with constant and oscillating boundary conditions

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

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