Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

scholarly journals Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 245
Author(s):  
Sabin Sathyan ◽  
Ugur Aydin ◽  
Anouar Belahcen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Finite Element Simulation ◽  
Acoustic Noise ◽  
The Finite Element Method ◽  
Magnetic Forces ◽  
Element Simulation ◽  
Element Method

This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

scholarly journals Elongation determination using finite element and boundary element method

2015 ◽  
Vol 61 (4) ◽  
pp. 389-394
Author(s):  
Piotr Kisała ◽  
Waldemar Wójcik ◽  
Nurzhigit Smailov ◽  
Aliya Kalizhanova ◽  
Damian Harasim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Experimental Studies ◽  
Numerical Algorithms ◽  
Mathematical Structure ◽  
The Finite Element Method ◽  
Fbg Sensor ◽  
Element Method

AbstractThis paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG.

Application of the Finite Element Method to Transient Flow in Porous Media

1968 ◽  
Vol 8 (03) ◽  
pp. 241-252 ◽  
Author(s):  
Iraj Javandel ◽  
P.A. Witherspoon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Steady State ◽  
Transient Flow ◽  
Energy Functional ◽  
Flow In Porous Media ◽  
The Finite Element Method ◽  
Potential Energy Functional ◽  
Element Method

Abstract The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite element method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling properties provides a new method of handling problems of fluid flow in complex systems. problems of fluid flow in complex systems Introduction Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach Wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. Clough has recently reviewed the application of the finite element method in the field of structural mechanics The technique has been applied successfully in the stress analysis of many complex structures. Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional leads naturally to its extension to other boundary value problems. problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles. By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung. Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface. The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems. SPEJ P. 241

Optimization of the Geometry of Shafts Using Boundary Elements

1984 ◽  
Vol 106 (2) ◽  
pp. 199-202 ◽  
Author(s):  
C. A. Mota Soares ◽  
H. C. Rodrigues ◽  
L. M. Oliveira Faria ◽  
E. J. Haug
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Programming ◽  
Boundary Element Method ◽  
Optimal Design ◽  
Boundary Elements ◽  
Linearization Method ◽  
Nonlinear Programming Problem ◽  
The Finite Element Method ◽  
Element Method

The problem of the optimization of the geometry of shafts is formulated in terms of boundary elements. The corresponding nonlinear programming problem is solved by Pshenichny’s Linearization method. The advantages of the boundary element method over the finite element method for optimal design of shafts are discussed, with reference to the applications.

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

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