Numerical modeling of twin tunnels under seismic loading using the Finite Difference Method and Finite Element Method

2021 ◽  
Author(s):  
Abdelhay El Omari ◽  
Mimoun Chourak ◽  
Seif-Eddine Cherif ◽  
Carlos Navarro Ugena ◽  
El Mehdi Echebba ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Seismic Loading ◽  
The Finite Difference Method ◽  
Twin Tunnels ◽  
Element Method

scholarly journals 1D Numerical modelling of dam break using finite element method

2019 ◽  
Vol 270 ◽  
pp. 04022 ◽  
Author(s):  
Nur Lely Hardianti Zendrato ◽  
Dhemi Harlan ◽  
Mohammad Bagus Adityawan ◽  
Dantje Kardana Natakusumah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Error Rate ◽  
Difference Method ◽  
Dam Break ◽  
Numerical Instability ◽  
Element Method

In numerical modeling, dam break is one case that has its own challenges, because shock wave is found in the dam break modeling that usually provides a numerical instability. Usually, dam break problem is solved by Saint Venant equation using a finite difference method with artificial dissipation or Total Variation Diminishing (TVD) filter. But in this research, finite element method and the finite difference method are used. To verify the accuracy of the model, a comparison against the Stoker analytical method for dam break case was performed. Numerical modeling of dam break is required to find out the collapse area, thus it is used for determining mitigation that can be done in the area, related to dam safety. In numerical modeling, oscillation or numerical instability often occurs, for which special treatment is required to reduce or eliminate the oscillations. In this research, the treatment for that case is a Hansen filter for both methods. From the simulation result, it is found that Hansen filter is sensitive in reducing oscillation depending on the correction factor value and Δt that used. For dam break case, after filter applied, the value of Pearson Correlation Coefficient of Taylor Galerkin and Mac-Cormack methods are 0.999. The error rate for a Taylor Galerkin method are 0.118% at t = 3s and 0.123% at t = 10s. The error rate for Mac-Cormack method are 0.043% at t = 3s and 5.048% at t = 10s. From the comparison of the model, it can be concluded that Taylor Galerkin finite element method proved to be capable and more accurate in simulating dam break compared to Mac-Cormack finite difference method.

GALERKIN FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD FOR SOLVING CONVECTIVE NON-LINEAR EQUATION

2010 ◽  
Vol 9 (1-2) ◽  
pp. 69
Author(s):  
E. C. Romão ◽  
M. D. De Campos ◽  
L. F. M. De Moura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Convection Diffusion ◽  
Non Linear ◽  
Element Method

The fast progress has been observed in the development of numerical and analytical techniques for solving convection-diffusion and fluid mechanics problems. Here, a numerical approach, based in Galerkin Finite Element Method with Finite Difference Method is presented for the solution of a class of non-linear transient convection-diffusion problems. Using the analytical solutions and the L2 and L∞ error norms, some applications is carried and valuated with the literature.

scholarly journals Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method

2021 ◽  
Vol 9 (9) ◽  
pp. 1397-1398
Author(s):  
Dr. A. R. Gupta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Comparative Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Rectangular Plate ◽  
Difference Method ◽  
Numerical Technique ◽  
Element Analysis ◽  
Element Method

Abstract: Plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a comparative analysis of rectangular plate is done between Finite Element Method (FEM) and Finite Difference Method (FDM). The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. The ordinary Finite Difference Method (FDM) is used to solve the governing differential equation of the plate deflection. The proposed methods can be easily programmed to readily apply on a plate problem. Keywords: Arbitrary, FEM, FDM, boundary.

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