Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling

Li, Jichun; Chen, Y.; Pepper, Darrell W.

doi:10.1007/s00466-003-0447-y

Cited by 72 publications

(30 citation statements)

References 14 publications

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“…From Fig. 4, it is observed that both the RPIM and analytical results, as well results from Li et al (2003) are in agreement with one another.…”

Section: Numerical Examplessupporting

confidence: 91%

“…The RPIM is applied to the problem considered by Li et al (2003). The model is applied to a soil column of horizontal length of 100 units with initial condition C (x, 0) = 0 and boundary conditions C (x, t) = 1.0 units at x = 0 and oC x;t ð Þ ox ¼ 0 at x = 100 units.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…and Boztosun et al ( , 2003 presented a meshfree method for solving advection-diffusion equation using a collocation method with thin plate radial basis functions. Li et al (2003) developed an algorithm based on a meshfree method for modelling water flow and contaminant transport using a collocation method with radial basis functions. Chinchapatnam et al (2006) investigated the application of unsymmetric and symmetric meshfree collocation techniques with radial basis functions for solving the unsteady convection-diffusion equation and compared the performance of various globally supported radial basis functions.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

Kumar

Dodagoudar

2009

Environ Earth Sci

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This paper presents a new numerical tool to model the two-dimensional contaminant transport through saturated porous media using a meshfree method, called radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes is needed. The advection-dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Three numerical examples are presented and the results are compared with those obtained from the finite element method and analytical solutions. In order to test the practical applicability and performance of the RPIM, two case studies of contaminant transport through landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

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“…From Fig. 4, it is observed that both the RPIM and analytical results, as well results from Li et al (2003) are in agreement with one another.…”

Section: Numerical Examplessupporting

confidence: 91%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

Kumar

Dodagoudar

2009

Environ Earth Sci

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“…The EFGM is applied to the problem considered by Li et al [19]. The model is applied to a soil column of horizontal length of 100 units with initial condition C(x, 0) = 0 and boundary conditions 672 R. PRAVEEN KUMAR AND G. R. DODAGOUDAR …”

Section: Example 2: Validation With Published Data: Advection-dispersionmentioning

confidence: 99%

“…Among all the meshfree methods, element-free Galerkin method (EFGM) has been successfully used for solving numerous boundary value problems related to various fields of study [11][12][13][14][15][16]. A limited amount of research is undertaken regarding the potential usage of the meshfree methods for modelling contaminant transport processes in the saturated porous media and in the area of landfill engineering [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Modelling of contaminant transport through landfill liners using EFGM

Kumar

Dodagoudar

2009

Num Anal Meth Geomechanics

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SUMMARYModelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advectiondominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data.

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A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

Shokri

Dehghan

2009

Numerical Methods Partial

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This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor-corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.

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Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling

Cited by 72 publications

References 14 publications

Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

Modelling of contaminant transport through landfill liners using EFGM

A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

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