Calculation of the Blade-to-Blade Compressible Flow Field in Turbo Impellers Using the Finite-Element Method

1977 ◽  
Vol 19 (3) ◽  
pp. 108-112 ◽  
Author(s):  
D. Adler ◽  
Y. Krimerman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Approach ◽  
Iterative Procedure ◽  
Coefficient Matrix ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Variational Functional ◽  
Linear Algebraic Equations ◽  
Computer Storage

No variational principle can be found for Wu's blade-to-blade equation and therefore no appropriate variational functional associated with the problem can be derived. This difficulty is overcome by using a Poisson equation as the basis for an iterative procedure. Thus the method retains the advantage of the variational approach in which the coefficient matrix of the linear algebraic equations is always symmetric. The symmetry of the coefficient matrix allows reduction of computer storage.

scholarly journals Application Of The Interlaced Sweep Method For The Solution Of Problems In Field Theory

2015 ◽  
Vol 3 ◽  
pp. 170
Author(s):  
Aloizs Ratnieks ◽  
Marina Uhanova
Keyword(s):  
Field Theory ◽  
Finite Element Method ◽  
Finite Element ◽  
Direct Methods ◽  
System Of Equations ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Sweep Method ◽  
Linear Algebraic Equations ◽  
Separate Block

<p class="R-AbstractKeywords"><span lang="EN-US">For solution of problems in field theory the method of sweep is very popular. The authors suggest a very effective method of interlaced sweep. The essence of the interlaced sweep method lies in the fact that matrix of the linear algebraic equations system is broken into parts and the solution of separate blocks is sought by direct methods. Usually for each line of the grid a separate block is created. The system of block equations has a tridiagonal matrix where only elements of the main diagonal and two neighboring diagonals are different from zero. The system of equations with such a matrix is easily solved by the method of elimination of unknowns.</span></p><p class="R-AbstractKeywords"><span lang="EN-US">By solving the problems by the finite element method, the nodes of touching of neighboring elements can be placed on curved lines, and the sweep on these lines can be performed observing the principle of interlaced sweep. By following this method, the neighboring lines should not belong to the same half-step.</span></p>

Schwarz Type Solvers for -FEM Discretizations of Mixed Problems

2012 ◽  
Vol 12 (4) ◽  
pp. 369-390
Author(s):  
Sven Beuchler ◽  
Martin Purrucker
Keyword(s):  
Finite Element ◽  
Stokes Problem ◽  
Schur Complement ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Contraction Ratio ◽  
Linear Algebraic Equations ◽  
Stokes Problems ◽  
Elasticity Problems ◽  
Element Pair

AbstractThis paper investigates the discretization of mixed variational formulation as, e.g., the Stokes problem by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development of an efficient preconditioner requires three ingredients, a preconditioner related to the components of the velocity modes, a preconditioner for the Schur complement related to the components of the pressure modes and a discrezation by a stable finite element pair which satisfies the discrete inf-sup-condition. The last condition is also important in order to obtain a stable discretization scheme. The preconditioner for the velocity modes is adapted from fast $hp$-FEM preconditioners for the potential equation. Moreover, we will prove that the preconditioner for the Schur complement can be chosen as a diagonal matrix if the pressure is discretized by discontinuous finite elements. We will prove that the system of linear algebraic equations can be solved in almost optimal complexity. This yields quasioptimal hp-FEM solvers for the Stokes problems and the linear elasticity problems. The latter are robust with respect to the contraction ratio ν. The efficiency of the presented solver is shown in several numerical examples.

An Analysis of the Large Deflections of Beams using the Rayleigh-Ritz Finite Element Method

1968 ◽  
Vol 19 (4) ◽  
pp. 357-367 ◽  
Author(s):  
A. C. Walker ◽  
D. G. Hall
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Large Deflection ◽  
Energy Functional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Comparison Of The Results ◽  
Element Method

SummaryThe Rayleigh-Ritz finite element method is used to obtain an approximate solution of the exact non-linear energy functional describing the large deflection bending behaviour of a simply-supported inextensible uniform beam subjected to point loads. The solution of the non-linear algebraic equations resulting from the use of this method is effected, using three different techniques, and comparisons are made regarding the accuracy and computing effort involved in each. A description is given of an experimental investigation of the problem and comparison of the results with those of the numerical method, and of the available exact continuum analyses, indicates that the numerical method provides satisfactory predictions for the non-linear beam behaviour for deflections up to one quarter of the beam’s length.

Stabilized numerical method for solving the Oseen type problem with a singularity

2018 ◽  
Author(s):  
А.В. Рукавишников
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Krylov Subspace ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Algebraic Equations ◽  
Type Problem ◽  
Curvilinear Boundary ◽  
Linear Algebraic Equations ◽  
Element Method

На основе метода декомпозиции области построен стабилизационный неконформный метод конечных элементов для решения задачи типа Озеена. Для конвективно доминирующих течений с разрывным коэффициентом вязкости определена шкала оптимального выбора стабилизирующего параметра. Результаты численных экспериментов согласуются с теоретической оценкой сходимости. Purpose. To construct modified approximation approach using the finite element method and to perform numerical analysis for a two dimensional problem on the flow of a viscous inhomogeneous fluids — the Oseen type problem, that is obtained by sampling in time and linearizing the incompressible Navier—Stokes equations. To consider the convection dominated flow case. Methodology. Based on the domain decomposition method with a smooth curvilinear boundary between subdomains, a stabilization nonconformal finite element method is constructed that satisfies the inf-sup-stability condition. To solve the resulting system of linear algebraic equations, an iterative process is considered that uses the decomposition of the vector in the Krylov subspace with minimal inviscidity, with a block preconditioning of the matrix. Findings. The results of the numerical experiments demonstrate the robustness of the considered method for different (even small) discontinuous values of viscosity. The differences between finite element and exact solutions for the velocity field and pressure in the norms of the grid spaces decrease as

Synthesis and Steady State Analysis of High-Speed Elastic Cam-Actuated Linkages by a Finite Element Method

1993 ◽  
Vol 115 (4) ◽  
pp. 800-807 ◽  
Author(s):  
Hsin-Ting J. Liu ◽  
D. R. Flugrad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Iterative Procedure ◽  
High Speed ◽  
The Finite Element Method ◽  
Linear Ordinary Differential Equations ◽  
Periodic Linear ◽  
Cam Profile ◽  
Design Speed ◽  
Element Method

A cam driving a lumped inertia through an elastic slider-crank follower linkage with a curved beam coupler is considered. An iterative procedure utilizing the finite element method developed by Midha et al. (1978) is used to synthesize the cam profile to produce a desired output motion at a given design speed and damping coefficient. Nonlinear terms are neglected producing inhomogeneous, periodic, linear, ordinary differential equations. Responses of the synthesized linkages are simulated and found to be satisfactory at the design conditions.

Calculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach

1986 ◽  
Vol 108 (3) ◽  
pp. 421-424 ◽  
Author(s):  
P. Klit ◽  
J. W. Lund
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Approach ◽  
Numerical Evaluation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Temperature Dependency ◽  
The Finite Element Method ◽  
Dynamic Coefficients ◽  
The Individual

The dynamic bearing coefficients are obtained from a solution to the variational equivalent of Reynolds equation. A perturbation method is applied to find the individual dynamic coefficients. The Finite Element Method is used in the numerical evaluation of the equations. The flow is assumed to be laminar, the lubricant is Newtonian. Allowance is made for viscosity-temperature dependency in circumferential and axial directions.

Sign in / Sign up

Export Citation Format

Share Document