scholarly journals Effect of Grid Step Sizes on Computational Time Using Finite-Difference Method for Seismic Wave Modeling

2016 ◽  
Vol 5 (2) ◽  
pp. 56
Author(s):  
Olowofela Joseph. A.
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Seismic Wave ◽  
Difference Method ◽  
Computational Time ◽  
Wave Modeling ◽  
Grid Step

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM

2014 ◽  
Vol 11 (04) ◽  
pp. 1350060 ◽  
Author(s):  
ZHIJIANG YUAN ◽  
LIANGAN JIN ◽  
WEI CHI ◽  
HENGDOU TIAN
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Computational Time ◽  
Algebraic Equations ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline for formulating the nonlinear equations and Jacobian matrix of towed system are proposed. We can solve the nonlinear dynamic equation of underwater towed system quickly by using this discipline, when the size of number elements is large.

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Anup Singh ◽  
S. Das ◽  
S. H. Ong ◽  
H. Jafari
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Conservative System ◽  
Computational Time ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nonlinear Reaction ◽  
Sink Term

In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.

The Simplified Method to Calculate Two-Dimensional Heat Conduction Equations of Heating Slab

2011 ◽  
Vol 79 ◽  
pp. 105-110
Author(s):  
Guo Jun Li ◽  
Xiao Ting Li ◽  
Hai Geng Chen
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Thermal Flux ◽  
Computational Time ◽  
Fourth Power ◽  
Heating Process ◽  
Two Dimensional ◽  
Simplified Method

The most effective way of determining the whole billet temperature field is to use a simulation model. Large amount of calculation as well as computational time is consumed to employ two-dimensional finite difference method since the heating process is extremely complex, then it’s necessary to simplify the calculation process. In this paper, a simplified method in one-dimension format was presented to calculate two-dimensional heat conduction equations of heating slab. The billet simulated was placed in a changeable thermal flux boundary environment, in which the thermal flux was proportional to fourth power of temperature. During the heating process, the changeable parameters were taken into account: i. e different billet dimensions, different billet thermal conduction, different specific heat, etc. The comparision between results of two-dimensional finite difference method and the simplified method verified that the simplified method can satisfy accuracy requirement as well as calculation time saving, which enable the simplified method online using.

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