Modifying Charge Input Optimization in Arc Surfacing with the Controlling Magnetic Influence

2014 ◽  
Vol 682 ◽  
pp. 298-303
Author(s):  
V.V. Peremit’ko ◽  
V.D. Kuznetsov ◽  
A.N. Sokol
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Finite Difference Method ◽  
Algebraic Equations ◽  
Simple Iteration ◽  
Bulk Force ◽  
Linear Algebraic Equations ◽  
Hydrodynamic Processes ◽  
The Finite Difference Method ◽  
Model Equations

The hydrodynamic processes modelling in the weld pool under the influence of the electromagnetic bulk force was carried out. For the approximation of the model equations the finite difference method was used. The resulting system of linear algebraic equations was solved by simple iteration. The finding served the basis for determining the optimal scheme supply of powder material adding for the modification and alloying of the weld (build-up) metal in the presence of an external magnetic field.

A Novel Finite Difference Method for Flow Calculation on Colocated Grids

2008 ◽  
Author(s):  
Z. Z. Xia ◽  
P. Zhang ◽  
R. Z. Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Fluid Dynamic ◽  
Algebraic Equations ◽  
Duct Flow ◽  
Staggered Grids ◽  
Linear Algebraic Equations ◽  
Incomplete Lu Factorization

A new finite difference method, which removes the need for staggered grids in fluid dynamic computation, is presented. Pressure checker boarding is prevented through a dual-velocity scheme that incorporates the influence of pressure on velocity gradients. A supplementary velocity resulting from the discrete divergence of pressure gradient, together with the main velocity driven by the discretized pressure first-order gradient, is introduced for the discretization of continuity equation. The method in which linear algebraic equations are solved using incomplete LU factorization, removes the pressure-correction equation, and was applied to rectangle duct flow and natural convection in a cubic cavity. These numerical solutions are in excellent agreement with the analytical solutions and those of the algorithm on staggered grids. The new method is shown to be superior in convergence compared to the original one on staggered grids.

scholarly journals Numerical Solution of Second-Order Fredholm Integrodifferential Equations with Boundary Conditions by Quadrature-Difference Method

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Chriscella Jalius ◽  
Zanariah Abdul Majid
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Numerical Experiments ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Gauss Elimination

In this research, the quadrature-difference method with Gauss Elimination (GE) method is applied for solving the second-order of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and second-order finite-difference method are used to discretize the second-order of LFIDEs. This approximation equation will be used to generate a system of linear algebraic equations and will be solved by using Gauss Elimination. In addition, the formulation and the implementation of the quadrature-difference method are explained in detail. Finally, some numerical experiments were carried out to examine the accuracy of the proposed method.

scholarly journals «TOMOGRAPHIC TRANSFORMATION» OF ANOMALOUS MAGNETIC FIELD USING GRID DISTRIBUTION OF EQUIVALENT SOURCES

2021 ◽  
pp. 10-23
Author(s):  
A.S. Dolgal ◽  
◽  
P. N. Novikova ◽  
E.N. Osipova ◽  
A.V. Pugin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Approximation ◽  
Analytical Approximation ◽  
Magnetic Survey ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Elevation Data ◽  
History Of ◽  
Equivalent Sources

The article is devoted to the «tomographic» approach to the interpretation of geopotential fields. A brief excursus into the history of the development of interpretational (pseudo-) tomography is given. General issues concerning the creation of «effective» tomographic models are considered. Transformations based on the equivalent source technique are proposed as a key part of the tomography. This type of transformations permits the usage of elevation data of magnetic survey as input. When constructing an analytical approximation, usually a system of linear algebraic equations (SLAE) with an approximated right part is solved. Using a model example, some issues concerning the conditionality of SLAE for different depths of equivalent sources are studied. Two iterative methods for the solving of systems, the Seidel method and the quickest gradient descent, are compared. It is shown that the latter method makes it possible to achieve the required accuracy of the field approximation with a smaller number of iterations. The advantage in the calculation speed, when the matrix of coefficients of the transform operator (source function) is sparce, is emphasized. An example of using this approach to interpret magnetic field anomalies above the submarine volcano 3.18 within the Kuril Iceland arc is presented.

Effect of magnetic field on the thermo-elastic response of a rotating FGM Circular disk with non-uniform thickness

2021 ◽  
pp. 030932472110052
Author(s):  
Pranta Rahman Sarkar ◽  
Akm Samsur Rahman
Keyword(s):  
Magnetic Field ◽  
Finite Difference Method ◽  
Outer Surface ◽  
Thermal Gradient ◽  
Radial Stress ◽  
Circumferential Stress ◽  
Circular Disk ◽  
Elastic Response ◽  
The Finite Difference Method ◽  
The Magnetic Field

In this study, the effect of the magnetic field on the thermo-elastic response of a rotating non-uniform circular disk of functionally graded material (FGM) is investigated for both steady and transient states of temperature. A single second-order ordinary differential equation of motion was developed for an FGM disk and solved along with the boundary conditions using the finite-difference method (FDM). The steady-state and transient heat conduction equations were also solved using the finite-difference method. Numerical results were presented and discussed for an Al/Al2O3 FGM disk of exponentially varying material properties keeping Poisson’s ratio and magnetic permeability uniform. Displacement and stress components were analyzed by increasing the intensity of the magnetic field for different cases of steady and transient states of temperature. The analysis suggests that the magnetic field has a remarkable effect on the displacement and stress distributions. It is also found that, high intensity of the magnetic field changes the nature and location of maximum stress. The transient analysis of magneto-thermo-elastic field suggests that the increase in the intensity of magnetic field results in the increase in stress intensity near the outer region of the disk and maximum radial stress always exceeds maximum circumferential stress. The effects of inner and outer surface radius, thermal gradient between inner and outer surface, and the outer surface thickness were also analyzed in detail. It was found that, with the decrease in outer surface radius and thermal gradient between inner and outer surface, maximum circumferential stress becomes higher than the maximum radial stress. In addition, the soundness and accuracy of the solutions were verified with the results from the standard computational method and analytical solution.

scholarly journals WO-GRID METHOD OF STRUCTURAL ANALYSIS BASED ON DISCRETE HAAR BASIS. PART 1: ONE-DIMENSIONAL PROBLEMS

2017 ◽  
Vol 13 (4) ◽  
pp. 128-139
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Grid Method ◽  
Algebraic Equations ◽  
Initial State ◽  
One Dimensional ◽  
Haar Basis ◽  
Linear Algebraic Equations

The distinctive paper is devoted to the two-grid method of structural analysis based on discrete Haar basis (in particular, the simplest one-dimensional problems are under consideration). A brief review of publications of recent years of Russian and foreign specialists devoted to the current trends in the use of wavelet analysis in construction mechanics is given. Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the detailing component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation (defined on a given interval) is a system of linear algebraic equations (SLAE) constructed within finite difference method (FDM) or the finite element method (FEM). Next, the transition to the resolving SLAE is done. Block Gauss method is used for its direct solution (forward-backward algorithm is realized). We consider a numerical solution of the boundary problem of bending of the Bernoulli beam lying on an elastic foundation (within Winkler model) as a practically important one-dimensional sample. There is good consistency of the results obtained by the proposed method and by standard finite difference method.

RECOIL IMPLANTATION MÖSSBAUER EXPERIMENT ON 57Fe IN Ge IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

1980 ◽  
Vol 41 (C1) ◽  
pp. C1-445-C1-445
Author(s):  
G. Langouche ◽  
N. S. Dixon ◽  
L. Gettner ◽  
S. S. Hanna
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Recoil Implantation
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