scholarly journals Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

2020 ◽  
Vol 10 (2) ◽  
pp. 439 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Yan Su ◽  
Luxi Yang ◽  
Wei-Po Huang
Keyword(s):  
Mesh Generation ◽  
Separation Of Variables ◽  
Basis Functions ◽  
Confined Aquifer ◽  
Groundwater Response ◽  
Time Marching ◽  
Collocation Approach ◽  
Comparison Of The Results ◽  
Set Of Points ◽  
Superposition Theorem

This paper presents the modeling of tide–induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing equation deriving from the separation of variables. The solution of the groundwater response in a coastal confined aquifer with an estuary boundary where the phase and amplitude of tide can vary with time and position is then approximated by the linear combination of Trefftz basis functions using the superposition theorem. The SCA is validated for several numerical examples with analytical solutions. The comparison of the results and accuracy for the SCA with the time–marching finite difference method is carried out. In addition, the SCA is adopted to examine the tidal and groundwater piezometer data at the Xing–Da port, Kaohsiung, Taiwan. The results demonstrate the SCA may obtain highly accurate results. Moreover, it shows the advantages of the SCA such that we only discretize by a set of points on the spacetime boundary without tedious mesh generation and thus significantly enhance the applicability.

scholarly journals Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3580
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Separation Of Variables ◽  
Time Integration ◽  
Meshfree Method ◽  
Space Time ◽  
Basis Functions ◽  
Trefftz Method ◽  
Dimensional Boundary

This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to validate the proposed approach. Emphasis is placed on the two-dimensional boundary detection problem in which the nonlinearity is solved using the fictitious time integration method. Results demonstrate that approximations with high accuracy are acquired in which the boundary data on the absent boundary may be efficiently recovered even when inaccessible partial data are provided.

Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method

2019 ◽  
Vol 20 (6) ◽  
pp. 703-712
Author(s):  
Naraveni Rajashekar ◽  
Sudhakar Chaudhary ◽  
V.V.K. Srinivas Kumar
Keyword(s):  
Mesh Generation ◽  
Numerical Experiments ◽  
Basis Functions ◽  
Spline Method ◽  
Biharmonic Problem ◽  
Difficult Time ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Low Dimensional ◽  
The Web

Abstract We describe and analyze the weighted extended b-spline (WEB-Spline) mesh-free finite element method for solving the p-biharmonic problem. The WEB-Spline method uses weighted extended b-splines as basis functions on regular grids and does not require any mesh generation which eliminates a difficult, time consuming preprocessing step. Accurate approximations are possible with relatively low-dimensional subspaces. We perform some numerical experiments to demonstrate the efficiency of the WEB-Spline method.

scholarly journals A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2595 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Weichung Yeih ◽  
Chia-Ming Fan
Keyword(s):  
Diffusion Equation ◽  
Meshless Method ◽  
Moving Boundary ◽  
Iterative Scheme ◽  
Separation Of Variables ◽  
Subsurface Flow ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Trefftz Method ◽  
Flow Problems

In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the superposition theorem using the basis functions, which match the data at the spacetime boundary collocation points. Because the proposed basis functions fully satisfy the diffusion equation, arbitrary nodes are collocated only on the spacetime boundaries for the discretization of the domain. The iterative scheme has to be used for solving the moving boundaries because the transient moving boundary problems exhibit nonlinear characteristics. Numerical examples, including harmonic and non-harmonic boundary conditions, are carried out to validate the method. Results illustrate that our method may acquire field solutions with high accuracy. It is also found that the method is advantageous for solving inverse problems as well. Finally, comparing with those obtained from the method of fundamental solutions, we may obtain the accurate location of the nonlinear moving boundary for transient problems using the spacetime meshless method with the iterative scheme.

The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation

2014 ◽  
Vol 24 (8) ◽  
pp. 1636-1659 ◽  
Author(s):  
Akbar Mohebbi ◽  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan
Keyword(s):  
Radial Basis Functions ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Basis Functions ◽  
Content Type ◽  
Fractional Telegraph Equation ◽  
Radial Basis ◽  
Collocation Approach ◽  
Derivatives Of

Purpose – The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation. Design/methodology/approach – In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives. Findings – The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy. Originality/value – The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

scholarly journals Simulation of Groundwater Response by Conceptual Models

1983 ◽  
Vol 14 (2) ◽  
pp. 71-84 ◽  
Author(s):  
Sten Bergström ◽  
Göran Sandberg
Keyword(s):  
General Model ◽  
Conceptual Models ◽  
Unconfined Aquifer ◽  
Model Structure ◽  
Confined Aquifer ◽  
Clay Deposit ◽  
Groundwater Response ◽  
Runoff Model

A conceptual runoff model is modified and applied to groundwater observations in an unconfined till aquifer, a confined aquifer under a clay deposit and a large unconfined esker aquifer. The results show that these types of aquifers can be modelled by one general model structure with only a few options. For the confined case the model is feasable for response simulation only while it gives a fair estimate of recharge of the unconfined aquifer.

Isogeometric Analysis for Tire Simulations: From Mesh Generation to High Precision Results

2021 ◽  
Author(s):  
Alina Israfilova ◽  
Mario A. Garcia ◽  
Michael Kaliske
Keyword(s):  
Mesh Generation ◽  
Isogeometric Analysis ◽  
Basis Functions ◽  
Model Generation ◽  
Element Analysis ◽  
New Approach ◽  
Vertical Stiffness ◽  
First Time ◽  
Further Development ◽  
Higher Order Functions

ABSTRACT Isogeometric analysis (IGA) has become an alternative to standard finite element analysis (FEA) in many areas of engineering. Its powerful tools for model generation and flexibility of basis functions make this relatively new approach attractive for tire analysis and its computational challenges. This contribution summarizes the benefits of IGA for complex tire simulations starting from model generation and the subsequent transition to the environment of numerical analysis without losing accuracy at the parametrizing stage. It presents results of further development work on earlier pioneering examples of the application of IGA in pneumatic tire analysis. In addition to the analysis of vertical stiffness, for the first time, velocity and acceleration fields are addressed and compared with experimental results and standard FEA simulations, with a focus on benefits of the continuity of basis functions within the contact patch. The numerical issues that arise in IGA at the enforcement of contact and the application of inelastic materials with inclusions of reinforcing layers are studied. Moreover, the important advantages of the possibility to use higher order functions for simulations of tire maneuvers are addressed within the steady-state framework. Numerical examples are provided to illustrate the capabilities of IGA. Concluding remarks on the results close the publication.

scholarly journals Fast Integral Equation Solution of Scattering of Multiscale Objects by Domain Decomposition Method with Mixed Basis Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ran Zhao ◽  
Hua Peng Zhao ◽  
Zai-ping Nie ◽  
Jun Hu
Keyword(s):  
Integral Equation ◽  
Domain Decomposition ◽  
Mesh Generation ◽  
Electromagnetic Scattering ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Equation Solution ◽  
Nonoverlapping Domain Decomposition ◽  
Well Posed

Nonconformal nonoverlapping domain decomposition method (DDM) with mixed basis functions is presented to realize fast integral equation solution of electromagnetic scattering of multiscale objects. The original multiscale objects are decomposed into several closed subdomains. The higher order hierarchical vector basis functions are used in the electrically large smooth subdomains to significantly reduce the number of unknowns, while traditional Rao-Wilton-Glisson basis functions are used for subdomains with tiny structures. A well-posed matrix is successfully derived by the present DDM. Besides, the nonconformal property of DDM allows flexible mesh generation for complicated objects. Numerical results are presented to validate the proposed method and illustrate its advantages.

Vibration Analysis of Laminated and Stepped Circular Arches by a Strong Formulation Spectral Collocation Approach

2016 ◽  
Vol 08 (03) ◽  
pp. 1650036 ◽  
Author(s):  
Xiang Xie ◽  
Hui Zheng ◽  
Haosen Yang
Keyword(s):  
Boundary Conditions ◽  
Haar Wavelet ◽  
Free Vibrations ◽  
Basis Functions ◽  
Spectral Collocation ◽  
Approximation Process ◽  
Arbitrary Boundary ◽  
Collocation Approach ◽  
And Function ◽  
Strong Formulation

A strong formulation-based spectral collocation approach is presented to investigate the statics and free vibrations of laminated and stepped arches with arbitrary boundary conditions even full rings. The influences of shear deformation, inertia rotary and deepness term are considered in the theoretical model. The basic concept of the present approach is the expansion of the highest derivatives appearing in the governing equations instead of solution function itself by adopted basis functions. Then lower order derivatives and function itself are obtained by integration. The constants arising from the integrating process are determined by given boundary conditions. Due to the approximation process based on integration technique rather than conventional differentiation, it does not require the basis function to be differentiable or continuous, which makes the choice of basis functions quite freely. The robustness of the approach for the application of various basis functions is evaluated by using Haar wavelet and Chebyshev orthogonal polynomials. To test the convergence, efficiency and accuracy of the approach, the numerical results are compared with those previously published in literature. Very good agreement can be observed. A distinctive feature of the proposed approach is its unified applicability for arbitrary elastic-supported boundary conditions.

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