The finite layer method for groundwater flow models

The finite-strip method (FSM) is a hybrid technique which combines spectral and finite-element methods. Finite-element approximations are made for each mode of a finite Fourier series expansion. The Galerkin formulated method is set apart from other weighted-residual techniques by the selection of two types of basis functions, a piecewise linear interpolating function and a trigonometric function. The efficiency of the FSM is due in part to the orthogonality of the complex exponential basis: The linear system which results from the weak formulation is decoupled into several smaller systems, each of which may be solved independently. An error analysis for the FSM applied to time-dependent, parabolic partial differential equations indicates the numerical solution error is O(h2 + W r ) .M represents the Fourier truncation mode number and h represents the finiteelement grid mesh. The exponent r 2 2 increases with the cxact solution smoothness in the respective dimension. This error estimate is verified computationally. Extending the result to the finite-layer method, where a two-dimensional trigonometric basis is used, the numerical solution error is O(h2 + M-' + N -4 ) . The N and q represent the truncation mode number and degree of exact solution smoothness in the additional dimension. GI 1993 John Wilev ti Sons. Inc.

show abstract

“…This decoupling allows one to solve for distinct Fourier modes in parallel, as demonstrated computationally in [2,4,5].…”

Section: (20)mentioning

confidence: 99%

Error analysis of the finite‐strip method for parabolic equations

Forde

Allen

1993

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

“…Smith et al [20] solved the groundwater flow problem discretizing two space dimensions using truncated Fourier series and approximating variations in the third dimension via the FE method. The eigenfunctions in the Fourier expansions are orthogonal; therefore, the Galerkin integrations decouple the weighted residual equations associated with different Fourier nodes.…”

mentioning

confidence: 99%

Solving the steady‐state groundwater flow equation for finite linear aquifers using a generalized Fourier series approach in two‐dimensional domains

Capilla¹,

Pulido-Velázquez²,

Sahuquillo³

et al. 2009

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA method to solve steady linear groundwater flow problems using generalized Fourier Series is developed and particularized for multiple Fourier series in two-dimensional domains. It leads to a linear vector equation whose solution provides a finite number of generalized Fourier coefficients approximating the hydraulic head field. Its implementation is shown and two relevant properties are found for the system matrix. It is always symmetric and, once computed, if additional Fourier terms are needed for a better approximation of the hydraulic head field, previously computed matrix elements remain invariant, i.e. only new rows and columns are added to the system matrix. The method is demonstrated in three simple cases with different geometries and transmissivity fields, where solutions are compared with analytical and finite element method results. Thus, the method is verified as an alternative to other flow solvers. Additionally, it provides a direct way to obtain the spectral form of the flow equation solution, given a spectral representation of transmissivity, and can be easily extended to obtain continuous velocity fields and their approximated spectral expressions.

show abstract

“…Meanwhile, soil consolidation and surface deformation entailing the extraction of water was also investigated by using this approach [24][25][26]. In the next several years, researchers applied the FLM in groundwater flow models [27] and analyses of 3D Biot consolidation of layered transversely isotropic soils [28]. Recently, the FLM was applied for modeling the noise transmission through double walls [29].…”

Section: Introductionmentioning

confidence: 99%

Application of Finite Layer Method in Pavement Structural Analysis

et al. 2017

View full text Add to dashboard Cite

Abstract:The finite element (FE) method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D) modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM) for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D) mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP) method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages.

show abstract

The finite layer method for groundwater flow models

Cited by 10 publications

References 12 publications

Error analysis of the finite‐strip method for parabolic equations

Error analysis of the finite‐strip method for parabolic equations

Solving the steady‐state groundwater flow equation for finite linear aquifers using a generalized Fourier series approach in two‐dimensional domains

Application of Finite Layer Method in Pavement Structural Analysis

Contact Info

Product

Resources

About