A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Wang, Qiang; Kim, Pyeoungkee; Qu, Wenzhen

doi:10.3390/math10030515

Cited by 5 publications

(4 citation statements)

References 59 publications

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“…Several examples of different types of dual interpolation elements are employed to verify the availability that the dual interpolation curve is reasonable and applicable to characterize continuous and discontinuous curve modeling in Section 5.2 and Section 5.3, respectively. According to the proposed method, relative errors measured in H 1 -norm and L2-norm [29,30] are given to demonstrate the accuracy and convergence of dual interpolation curves, which are defined as:…”

Section: Resultsmentioning

confidence: 99%

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

et al. 2023

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The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

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Section: Resultsmentioning

confidence: 99%

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

et al. 2023

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“…where C 7 , C 8 , and C 9 are constants, and J 0 and Y 0 denote the Bessel functions of the first and second kind, respectively. By substituting Equation (19) into Equation (1), we arrive at the following expression:…”

Section: Basis Function For the Axisymmetric Transient Groundwater Fl...mentioning

confidence: 99%

“…Although mesh-generation techniques can be employed to solve axisymmetric flow problems, they necessitate the use of extremely dense meshes to achieve satisfactory accuracy [15,16]. Meshfree methods were found to be highly promising as competitive alternatives due to their simplicity in characterization and flexibility in solving inverse problems through boundary collocation points, resulting in reduced computational complexity [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Novel Spacetime Boundary-Type Meshless Method for Estimating Aquifer Hydraulic Properties Using Pumping Tests

Ku,

Liu

2023

Mathematics

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This article introduces a new boundary-type meshless method designed for solving axisymmetric transient groundwater flow problems, specifically for aquifer tests and estimating hydraulic properties. The method approximates solutions for axisymmetric transient groundwater flow using basis functions that satisfy the governing equation by solving the inverse boundary value problem in the spacetime domain. The effectiveness of this method was demonstrated through validation with the Theis solution, which involves transient flow to a well in an infinite confined aquifer. The study included numerical examples that predicted drawdown at various radial distances and times near pumping wells. Additionally, an iterative scheme, namely, the fictitious time integration method, was employed to iteratively determine the hydraulic properties during the pumping test. The results indicate that this approach yielded highly accurate solutions without relying on the conventional time-marching scheme. Due to its temporal and spatial discretization within the spacetime domain, this method was found to be advantageous for estimating crucial hydraulic properties, such as the transmissivity and storativity of an aquifer.

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“…In this context, a hybrid meshless method that coupled the hybrid boundary node method with the dual reciprocity method was proposed for solving the Helmholtztype equation [79]. More recently, a hybrid localised meshless method has been developed and formulated by mixing the generalised finite difference method and the Crank-Nicolson scheme for solving transient groundwater flow [80]. In this context, the hybridisation of SBM and MFS approaches is a novel methodology that will be studied in this work.…”

Section: Alternative Meshless Approachesmentioning

confidence: 99%

Advanced 2.5D meshless methodologies to deal with soil-structure interaction problems in elastodynamics

Liravi

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This thesis is concerned with the development of efficient and practical numerical methodologies to deal with longitudinally invariant soil-structure interaction problems in elastodynamics. All the approaches appearing in this thesis are formulated in the frequency-wavenumber domain. Moreover, the formulations can deal with full-space and half-space models of the soil. The novel proposed methods are mainly based on meshless approaches, which provide three main benefits: simplicity on the formulation and implementation, to avoid meshing requirements and to increase the computational efficiency of the evaluation of the soil-structure system response. Generally, these approaches are employed to model the wave propagation in unbounded mediums. Thus, in this thesis, meshless methods are used to model the soil, while the finite element method is mainly used to deal with the structure modelling. However, this thesis also demonstrates that meshless methods can also be used to model homogeneous structures. The performances of the novel approaches presented have been assessed in the context of railway tunnels embedded in the soil, especially for the case studies of circular and cut-and-cover tunnels. The studies are carried out for different elastodynamic models of the soil, including homogeneous full-space, homogeneous half-space and horizontally layered half-space. Four new methodologies are presented in this thesis. Firstly, a two-and-a-half-dimensional finite element-boundary element methodology coupled with the method of fundamental solutions is developed. This approach uses the method of fundamental solutions to model the wave propagation in the soil once the soil-tunnel interaction has been determined, reducing the computational needs of computing the soil response. Afterwards, the second methodology further enhances the computational efficiency, the robustness and the simplicity of the approach, by modelling the soil response using the singular boundary method. To reach even higher computational benefits, a hybrid method that combines the singular boundary method and the method of fundamental solutions is proposed. This hybrid approach is found to be inheriting the computational efficiency of the method of fundamental solutions while keeping the robustness and accuracy presented by the singular boundary method. The hybrid methodology is finally extended to model both the structure and wave propagation in the soil, which leads to a fully meshless and efficient approach to deal with the soil-structure interaction problems. Esta tesis se centra en el desarrollo de metodologías numéricas prácticas y eficientes para tratar con problemas de interacción sólido-estructura longitudinalmente invariantes en elastodinámica. El conjunto de enfoques que aparecen en esta tesis está formulado en el dominio de la frecuencia y del número de onda. Además, las formulaciones pueden tratar el terreno con modelos de espacio completo y con modelos de semiespacio. Los nuevos métodos propuestos están principalmente basados en enfoques sin malla, los cuales aportan tres beneficios principales: simplicidad en la formulación e implementación, evitar los requisitos del mallado y un incremento de la eficiencia computacional requerida por la evaluación de la respuesta del sistema terreno-estructura. Generalmente, estos enfoques se emplean para modelizar la propagación de ondas en medios infinitos. Debido a esto, en esta tesis, los métodos sin malla se usan para modelizar el terreno, mientras que el método de los elementos finitos se usa principalmente para tratar con la modelización de la estructura. Sin embargo, esta tesis también demuestra que los métodos sin malla también se pueden usar para modelizar estructuras homogéneas. El desempeño de los nuevos enfoques presentados ha sido evaluado en el contexto de túneles ferroviarios en el terreno, en especial para los casos de túneles circulares y túneles cut-and-cover. Los estudios han sido realizados para distintos tipos de modelos elastodinámicos del terreno, incluyendo espacios completos, semiespacios homogéneos y semiespacios con estratificación horizontal. En esta tesis se presentan cuatro metodologías nuevas. Inicialmente, se desarrolla una metodología dos-y-medio-dimensional de elementos finitos con elementos de contorno acoplada con el método de las soluciones fundamentales. Este enfoque usa el método de las soluciones fundamentales para representar la propagación de ondas en el terreno una vez la interacción terreno-estructura ha sido determinada, reduciendo los requerimientos computacionales del cálculo de la respuesta del terreno. Posteriormente, la segunda metodología mejora aún más la eficiencia computacional, la robustez y la simplicidad del enfoque con la modelización de la respuesta del terreno usando el singular boundary method. Para obtener ventajas computacionales superiores, se propone un modelo híbrido que combina el singular boundary method con el método de las soluciones fundamentales. Se comprueba que este enfoque híbrido hereda la eficiencia computacional del método de las soluciones fundamentales manteniendo la robustez y precisión presentada por el singular boundary method. Finalmente, la metodología híbrida se extiende a la modelización de tanto la estructura como de la propagación de ondas en el terreno, llevando a un enfoque completamente sin malla y eficiente para tratar con problemas de interacción terreno-estructura.

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A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Cited by 5 publications

References 59 publications

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

A Novel Spacetime Boundary-Type Meshless Method for Estimating Aquifer Hydraulic Properties Using Pumping Tests

Advanced 2.5D meshless methodologies to deal with soil-structure interaction problems in elastodynamics

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