scholarly journals Analysis free surface of nonlinear seepage using the MQRBF method

2021 ◽  
Vol 233 ◽  
pp. 03042
Author(s):  
Yan SU ◽  
Yan SU ◽  
Zhi-ming ZHENG ◽  
Cheng-yu GU ◽  
Long-teng ZHANG
Keyword(s):  
Free Surface ◽  
Numerical Solution ◽  
Solution Process ◽  
Earth Dam ◽  
Richards Equation ◽  
Boundary Values ◽  
Base Function ◽  
Trefftz Method ◽  
Transient Problem ◽  
Radial Base Function

In order to solve the characteristics of low accuracy and slow efficiency in traditional numerical solution the free surface problem, the multiquardatic radial base function collocation method(MQ RBF) is used to analyze the constant seepage and unsteady seepage of the homogeneous earth dam. Computation of transient problem of free surface of earth dam by the linear derivation of Richards equation. The results show that the calculation accuracy of the MQRBF is higher than that of the traditional numerical method. The solution process does not involve numerical integral calculation and grid reorganization, which greatly reduces the calculation amount. Compared with the Trefftz method, it has the advantage of solving boundary values and internal values at the same time. It is not limited by the solution of the Laplace equation, and its application is wider and simpler.

scholarly journals Numerical analysis of coupled hydrosystems based on an object-oriented compartment approach

2008 ◽  
Vol 10 (3) ◽  
pp. 227-244 ◽  
Author(s):  
Olaf Kolditz ◽  
Jens-Olaf Delfs ◽  
Claudius Bürger ◽  
Martin Beinhorn ◽  
Chan-Hee Park
Keyword(s):  
Numerical Solution ◽  
Land Surface ◽  
Overland Flow ◽  
Drainage Basin ◽  
Spatial Scales ◽  
Shallow Water Equation ◽  
Object Oriented ◽  
Richards Equation ◽  
Saturated Flow ◽  
Flow Processes

In this paper we present an object-oriented concept for numerical simulation of multi-field problems for coupled hydrosystem analysis. Individual (flow) processes modelled by a particular partial differential equation, i.e. overland flow by the shallow water equation, variably saturated flow by the Richards equation and saturated flow by the groundwater flow equation, are identified with their corresponding hydrologic compartments such as land surface, vadose zone and aquifers, respectively. The object-oriented framework of the compartment approach allows an uncomplicated coupling of these existing flow models. After a brief outline of the underlying mathematical models we focus on the numerical modelling and coupling of overland flow, variably saturated and groundwater flows via exchange flux terms. As each process object is associated with its own spatial discretisation mesh, temporal time-stepping scheme and appropriate numerical solution procedure. Flow processes in hydrosystems are coupled via their compartment (or process domain) boundaries without giving up the computational necessities and optimisations for the numerical solution of each individual process. However, the coupling requires a bridging of different temporal and spatial scales, which is solved here by the integration of fluxes (spatially and temporally). In closing we present three application examples: a benchmark test for overland flow on an infiltrating surface and two case studies – at the Borden site in Canada and the Beerze–Reusel drainage basin in the Netherlands.

scholarly journals Modelling Unsaturated Flow in Porous Media Using an Improved Picard Iteration Scheme

2021 ◽  
Author(s):  
S.R. Zhu ◽  
L.Z. Wu ◽  
T. Ma ◽  
S.H. Li
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Unsaturated Flow ◽  
Control Volume ◽  
Linear Equations ◽  
Solution Process ◽  
Coefficient Matrix ◽  
Picard Iteration ◽  
Flow In Porous Media ◽  
Richards Equation

Abstract The numerical solution of various systems of linear equations describing fluid infiltration uses the Picard iteration (PI). However, because many such systems are ill-conditioned, the solution process often has a poor convergence rate, making it very time-consuming. In this study, a control volume method based on non-uniform nodes is used to discretize the Richards equation, and adaptive relaxation is combined with a multistep preconditioner to improve the convergence rate of PI. The resulting adaptive relaxed PI with multistep preconditioner (MP(m)-ARPI) is used to simulate unsaturated flow in porous media. Three examples are used to verify the proposed schemes. The results show that MP(m)-ARPI can effectively reduce the condition number of the coefficient matrix for the system of linear equations. Compared with conventional PI, MP(m)-ARPI achieves faster convergence, higher computational efficiency, and enhanced robustness. These results demonstrate that improved scheme is an excellent prospect for simulating unsaturated flow in porous media.

scholarly journals Predicting construction labor productivity using lower upper decomposition radial base function neural network

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Sasan Golnaraghi ◽  
Osama Moselhi ◽  
Sabah Alkass ◽  
Zahra Zangenehmadar
Keyword(s):  
Neural Network ◽  
Labor Productivity ◽  
Base Function ◽  
Lower Upper ◽  
Radial Base Function

scholarly journals Comparative Study of Analytic Solution and Numerical Solution of Baseband Symbol Signal Based on Optimal Generic Function

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mingxin Liu ◽  
Wei Xue ◽  
Sergey B. Makarov ◽  
Junwei Qi ◽  
Beiming Li
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Solution Process ◽  
Development Trend ◽  
Partial Solution ◽  
Research Process ◽  
Constraint Condition ◽  
Energy Limit ◽  
Function Model ◽  
Boundary Constraints

In this paper, the optimal mathematical generic function model is established using the minimum out-of-band energy radiation criterion. Firstly, the energy limit conditions, boundary constraints, and peak-to-average ratio constraints are applied to the generic function model; thus, the analytical solutions are obtained under different parameters. Secondly, a single symbol signal energy constraint condition and boundary constraint condition are added to the generic function model; thus, the numerical solution of the different parameters is obtained. In the process of solving the analytical solution, the partial solution process is simplified to solve the analytical solution, and there are also digital truncation problems. In addition, the corresponding order of the Lagrange differential equation increases by a multiple of 2 when the parameter n increases, which makes the solution extremely complicated or even impossible to solve. The numerical solution is in line with the current development trend of digital communication, and there is no need to simplify the solution process in the process of solving the numerical solution. When the parameter n and the Fourier series m take different values, the obtained symbol signals can also meet the needs of different communication occasions. The relevant data of the above research process were solved by a MATLAB software simulation, which proves the correctness of the method and the superiority of the numerical method.

scholarly journals A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing-En Xiao ◽  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Wei-Chung Yeih
Keyword(s):  
Free Surface ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Domain Decomposition Method ◽  
Subsurface Flow ◽  
Test Problems ◽  
Pressure Potential ◽  
Trefftz Method ◽  
Flow Problems ◽  
Boundary Type

A novel boundary-type meshless method for modeling geofluid flow in heterogeneous geological media was developed. The numerical solutions of geofluid flow are approximated by a set of particular solutions of the subsurface flow equation which are expressed in terms of sources located outside the domain of the problem. This pioneering study is based on the collocation Trefftz method and provides a promising solution which integrates the T-Trefftz method and F-Trefftz method. To deal with the subsurface flow problems of heterogeneous geological media, the domain decomposition method was adopted so that flux conservation and the continuity of pressure potential at the interface between two consecutive layers can be considered in the numerical model. The validity of the model is established for a number of test problems. Application examples of subsurface flow problems with free surface in homogenous and layered heterogeneous geological media were also carried out. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for solving subsurface flow with nonlinear free surface in layered heterogeneous geological media even with large contrasts in the hydraulic conductivity.

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