Unsteady Surface Element Method

1981 ◽  
Vol 103 (4) ◽  
pp. 759-764 ◽  
Author(s):  
N. R. Keltner ◽  
J. V. Beck
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Finite Difference ◽  
Transient Heat Conduction ◽  
The Other ◽  
Surface Element ◽  
Contact Conductance ◽  
The Given ◽  
Duhamel’S Integral ◽  
Element Method

A method for the solution of transient heat conduction problems, called the unsteady surface element (USE) method, is developed and applied to several problems. The method is intended for thermally contacting bodies of similar or dissimilar geometries such as occur in contact conductance and intrinsic thermocouple problems. The method utilizes Duhamel’s integral in several ways. Two different procedures are presented, one utilizing temperature-based kernels and the other uses heat flux-based kernels. One of the given applications is to the intrinsic thermocouple problem. Several solutions are given and the results agree very well with two finite difference solutions.

scholarly journals Finite Element Analysis of Square Aquifers Containing Pumped Wells and Comparison with Finite Difference Method

1983 ◽  
Vol 14 (2) ◽  
pp. 85-92 ◽  
Author(s):  
Tilahun Aberra
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Discrete Time ◽  
Surface Element ◽  
Dimensionless Time ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Wide Range ◽  
Element Method

The numerical solution of the behaviour of discrete time steps in digital computer analysis of square aquifers containing pumped wells is examined by using the finite element method with a 4 node linear quadrilateral isoparametric surface element. A wide range of time steps are used in the computation. The calculations show that discrete time steps can cause errors and oscillations in the calculations particularly when wells start and stop pumping. Comparison with known results obtained by theoretical and finite difference procedures has been considered. The main objective of this paper is to demonstrate comparison of the finite element and finite difference simulation results over a regular linear 4 node quadrilateral mesh suitable to represent the two numerical schemes with a marked similarity. The dimensionless time drawdown results of the finite element method agreed well with the finite difference and analytical results for small time increment. However, for large time increments, there are from slight to significant oscillations in the results and notable discrepancies are observed in the solutions of the two numerical methods.

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