An Efficient Algorithm for Fluid Force and its Jacobian Matrix in Journal Bearing

2005 ◽  
Vol 128 (2) ◽  
pp. 291-295 ◽  
Author(s):  
Zhonghui Xiao ◽  
Liping Wang ◽  
Tiesheng Zheng
Keyword(s):  
Efficient Algorithm ◽  
Journal Bearing ◽  
Jacobian Matrix ◽  
Direct Method ◽  
Current Method ◽  
Computational Time ◽  
Operational Characteristic ◽  
Algebraic Equations ◽  
Fluid Force ◽  
Linear Algebraic Equations

Based on the theory of variational inequality, a rapid efficient algorithm for fluid force and its Jacobian matrix in journal bearing is presented in this paper. Primarily, to solve the fluid force is transformed to solve a set of linear algebraic equations with tri-diagonal coefficient matrices. Meanwhile, an amendatory direct-method is proposed to solve the united equations about fluid forces and their Jacobian matrices, rapidly and synchronously. The Reynolds boundary condition has to be satisfied automatically during the process. Secondly, the coefficient matrices, which are involved in the previous process, can be decomposed to an assembly of a part of relative with journal motion and a part of invariable matrix, which can be prepared in advance and be referred to later repeatedly. Through these measures, many redundant operations are avoided. The numerical examples show that, under the accuracy guaranteed, the algorithm in this paper can reduce computational time remarkably, which reveals that the current method has a good operational characteristic and practicability.

Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations

1991 ◽  
Vol 113 (4) ◽  
pp. 681-688 ◽  
Author(s):  
Oktay Baysal ◽  
Mohamed E. Eleshaky
Keyword(s):  
Sensitivity Analysis ◽  
Euler Equations ◽  
Analytical Approach ◽  
Direct Method ◽  
Pressure Coefficient ◽  
Mathematical Formulation ◽  
Computational Time ◽  
Algebraic Equations ◽  
Sensitivity Coefficients ◽  
Linear Algebraic Equations

A mathematical formulation is developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible, two-dimensional Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. Two approaches to determine the aerodynamic sensitivity coefficients, namely, the finite difference approach, and the quasi-analytical approach are discussed with regards to their relative accuracies and involved computational efforts. In the quasi-analytical approach, the direct and the adjoint variable methods are formulated and assessed. Also, several methods to solve the system of linear algebraic equations, that arises in the quasi-analytical approach, are investigated with regards to their accuracies, computational time and memory requirements. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flow-field solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

ON SOFTWARE IMPROVEMENT OF IMAGE CHANNEL SUPPRESSION IN SDR RECEIVERS WITH ANALOG CONVERSION TO A LOW INTERMEDIATE FREQUENCY

2020 ◽  
pp. 45-52
Author(s):  
A. S. Yurkov
Keyword(s):  
Signal Processing ◽  
Direct Method ◽  
Digital Signal ◽  
Intermediate Frequency ◽  
Algebraic Equations ◽  
Recursive Filter ◽  
Linear Algebraic Equations ◽  
Reception Channel ◽  
Image Channel ◽  
Parasitic Phase

A method for digital signal processing in SDR receivers with analog conversion to a low intermediate frequency is proposed. In contrast to known systems, the proposed approach does not consider parasitic phase and amplitude distortions, but uses the direct method minimizing of the signal of the mirror reception channel. Generally speaking, this can be done simultaneously at several frequencies. It is shown that in computational terms, this is reduced to signal processing by an algorithm similar to a digital non-recursive filter, and to determine its coefficients, it is sufficient to solve a system of linear algebraic equations.

CONTINUOUS NEWTON METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATION

2010 ◽  
Vol 24 (13) ◽  
pp. 1303-1306
Author(s):  
Q.-D. CAI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Newton Method ◽  
Jacobian Matrix ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Non Linear System ◽  
Continuous Newton Method

Newton method is a widely used iteration method in solving nonlinear algebraic equations. In this method, a linear algebraic equations need to be solved in every step. The coefficient matrix of the algebraic equations is so-called Jacobian matrix, which needs to be determined at every step. For a complex non-linear system, usually no explicit form of Jacobian matrix can be found. Several methods are introduced to obtain an approximated matrix, which are classified as Jacobian-free method. The finite difference method is used to approximate the derivatives in Jacobian matrix, and a small parameter is needed in this process. Some problems may arise because of the interaction of this parameter and round-off errors. In the present work, we show that this kind of Newton method may encounter difficulties in solving non-linear partial differential equation (PDE) on fine mesh. To avoid this problem, the continuous Newton method is presented, which is a modification of classical Newton method for non-linear PDE.

scholarly journals Flow modelling in a straight hard-walled duct with two rectangular axisymmetric narrowings

2020 ◽  
Keyword(s):  
Computational Time ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Order Of Accuracy ◽  
First Order ◽  
Flow Modelling ◽  
Computational Mesh ◽  
Linear Algebraic Equations ◽  
Stability Of The Solution

A method for modelling the flow in a rigid-walled duct with two narrowings has been developed. It has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of the solution, and compared to the similar methods requires much less computational time to obtain a result. According to the method, the stream function and the vorticity are introduced initially, and consequently the transition from the governing equations, as well as the initial and boundary conditions to the proper relationships for the introduced variables is performed. The obtained relationships are rewritten in a non-dimensional form. After that a computational domain and a uniform computational mesh are chosen, and the corresponding discretization of the non-dimensional relationships is performed. Finally, the linear algebraic equations obtained as a result of the discretization are solved.

Heat and mass transfer analysis in unsteady titanium dioxide nanofluid between two orthogonally moving porous coaxial disks: a numerical study

2015 ◽  
Vol 93 (3) ◽  
pp. 290-299 ◽  
Author(s):  
Muhammad Farooq Iqbal ◽  
Kashif Ali ◽  
Muhammad Ashraf
Keyword(s):  
Mass Transfer ◽  
Titanium Dioxide ◽  
Heat And Mass Transfer ◽  
Numerical Study ◽  
Titanium Dioxide Nanoparticles ◽  
Direct Method ◽  
Fluid Velocity ◽  
Algebraic Equations ◽  
Electrically Conducting ◽  
Linear Algebraic Equations

Study of heat and mass transfer in an unsteady hydromagnetic viscous electrically conducting incompressible water-based nanofluid (containing titanium dioxide nanoparticles) between two orthogonally moving porous coaxial disks with suction and viscous dissipation effects. A combination of iterative and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the finite difference discretization of the quasi-linearized self-similar ordinary differential equations. It has been noticed that the rate of mass transfer at the disks decreases with the permeability Reynolds number; either the disks are approaching or receding. Moreover, the external magnetic field remarkably reduces the fluid velocity and therefore may be used as a controlling agent for the flow.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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