2-D resistivity modeling: An approach to arrays parallel to the strike direction

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 941-950 ◽  
Author(s):  
P. Queralt ◽  
J. Pous ◽  
A. Marcuello
Keyword(s):  
Mixed Boundary ◽  
Electrical Potential ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Exponential Functions ◽  
Direction Parallel ◽  
Strike Direction ◽  
Resistivity Modeling ◽  
Shape Of Potential

An algorithm for two‐dimensional electrical resistivity modeling using the finite‐element method with mixed boundary conditions can calculate the electrical potential along any arbitrary direction. In the particular case of the direction parallel to the strike of the structure, a numerical singularity occurs. We resolved it by calculating the potential near the singularity and improving the involved interpolation of the transformed potential. Investigating the shape of potential in the Fourier transformed space, we conclude that this interpolation may combine logarithmic and exponential functions.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

scholarly journals Fluctuations of the membrane with piecewise smooth contour and mixed boundary conditions

Vestnik MGSU ◽  
2015 ◽  
pp. 29-37
Author(s):  
Sergey Dmitrievich Algazin
Keyword(s):  
Mixed Boundary ◽  
A Priori ◽  
Numerical Algorithms ◽  
Mixed Boundary Conditions ◽  
Computing Methods ◽  
Piecewise Smooth ◽  
Two Dimensional ◽  
Calculation Algorithm ◽  
Smooth Contour ◽  
Priori Information

The eigenvalue problem for the two-dimensional operator Laplace is classical in mathematics and physics. However, computing methods for calculation of eigenvalues have still many problems, especially in applications to acoustic and electromagnetic wave guides. The investigated below two-dimensional spectral for the Laplace operator have been previously considered by the author only in smooth areas. The solutions of these tasks (eigen functions) are infinitely differentiated or. even analytical and therefore in order to create effective algorithms it is necessary to consider this enormous a priori information. Traditional methods of finite differences and finite elements almost do not practically use the information on smoothness of the decision, i.e. these are methods with saturation. The term “saturation” was entered by K.I. Babenko. Using the method of computing experiment the author investigates the task about fluctuations of the membrane with the piecewise smooth contour for two-dimensional area, obtained by conformal representation of the square. It is shown that eigen functions are infinitely differentiated. Therefore, numerical algorithms without saturation are applicable. In article the calculation algorithm of eigenvalues in this two-dimensional area is developed, which allows determining up to 10 natural frequencies with the accuracy acceptable for practice on the grid 10×10.

scholarly journals Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

2007 ◽  
Vol 15 (3) ◽  
pp. 157-172 ◽  
Author(s):  
Jonas Koko
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Linear Elasticity ◽  
Numerical Experiments ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Linear Finite Element ◽  
Matlab Implementation

A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

Relaxation Methods Applied to Two Problems of Two-Dimensional Stress Distribution Involving Mixed Boundary Conditions

1948 ◽  
Vol 1 (2) ◽  
pp. 135
Author(s):  
WH Wittrick ◽  
W Howard
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Relaxation Methods

Relaxation methods have been used to determine the stress distributions in both a rectangular and a highly tapered plate under tension when the load is applied through absolutely rigid clamps. Both problems require the treatment of boundary conditions involving the values of both stresses and displacements. The solutions were obtained in terms of displacements and the stresses were subsequently determined from them.

A Set of Orthogonal Plate Functions for Flexural Vibration of Regular Polygonal Plates

1991 ◽  
Vol 113 (2) ◽  
pp. 182-186 ◽  
Author(s):  
K. M. Liew ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Mixed Boundary ◽  
Flexural Vibration ◽  
Mixed Boundary Conditions ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simply Supported ◽  
Free Boundary Conditions

A computationally efficient and very accurate numerical method is proposed for vibration analysis of regular polygonal plates with any combinations of clamped, simply-supported and free boundary conditions. The method involves the use of two-dimensional orthogonal polynomials generated by the Gram-Schmidt recurrence procedure. For the cases of simply supported and fully clamped hexagonal and octagonal plates, the results obtained agreed very well with those existing in the literature. The frequencies and mode shapes for several hexagonal and octagonal plates subjected to mixed boundary conditions are also presented.

Sign in / Sign up

Export Citation Format

Share Document