A two-step explicit solution of the Boussinesq equation for efficient simulation of unconfined aquifers in conjunctive-use models

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.

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Towards a More Efficient Simulation of Surface-Groundwater Interaction in Conjunctive Use Systems: Selective Compression and Modal Masking in the Eigenvalue Method

Lecture Notes in Earth System Sciences - Mathematics of Planet Earth ◽

10.1007/978-3-642-32408-6_97 ◽

2013 ◽

pp. 439-442

Author(s):

Oscar David Álvarez-Villa ◽

Eduardo Cassiraga ◽

Andrés Sahuquillo

Keyword(s):

Conjunctive Use ◽

Efficient Simulation ◽

Eigenvalue Method

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Series representation of flux for the Boussinesq equation

Water Resources Research ◽

10.1029/90wr01696 ◽

1990 ◽

Vol 26 (12) ◽

pp. 2881-2886

Author(s):

P. Tolinkas

Keyword(s):

Boussinesq Equation ◽

Series Representation

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Reconstruction of complex shaped crack from ECT signals based on a fast forward solver using an advanced multi-media element

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209372 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 621-629

Author(s):

Yingsong Zhao ◽

Cherdpong Jomdecha ◽

Shejuan Xie ◽

Zhenmao Chen ◽

Pan Qi ◽

...

Keyword(s):

Coefficient Matrix ◽

Crack Edge ◽

Numerical Accuracy ◽

Gauss Point ◽

Current Testing ◽

Efficient Simulation ◽

Shaped Crack ◽

Multi Media ◽

Profile Reconstruction ◽

Crack Profile

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.

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