Approximate Solutions of Compressible Flows Past Bodies of Revolution by Variational Method

1951 ◽  
Vol 18 (3) ◽  
pp. 260-266
Author(s):  
Chi-Teh Wang ◽  
Socrates De Los Santos
Keyword(s):  
Variational Method ◽  
Arbitrary Shape ◽  
Compressible Flows ◽  
Direct Method ◽  
Approximate Solutions ◽  
Body Of Revolution ◽  
Approximate Methods ◽  
Bodies Of Revolution ◽  
Numerical Examples ◽  
Ellipsoid Of Revolution

Abstract Using the direct method of Rayleigh-Ritz in the calculus of variations, the problem of steady irrotational compressible flow past a body of revolution of arbitrary shape is formulated. In order to compare with the analytical solutions obtained by other investigators, two numerical examples have been carried out, namely, compressible flows past a sphere, and an ellipsoid of revolution. The results are found to be in excellent agreement with those computed by other approximate methods.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

Investigation of the Influence of Inertia Forces on the Adhesion of the Coating to the Outer Surface of Bodies of Revolution during Thermal Spraying

2021 ◽  
Vol 316 ◽  
pp. 726-731
Author(s):  
Alexey Yu. Rodichev ◽  
Roman N. Polyakov ◽  
Andrey V. Gorin
Keyword(s):  
Adhesion Strength ◽  
Outer Surface ◽  
External Surface ◽  
Thermal Spraying ◽  
Inertial Forces ◽  
Body Of Revolution ◽  
Mathematical Apparatus ◽  
Bodies Of Revolution ◽  
Steel Base ◽  
Inertia Forces

The article presents the results of a study of the influence of inertial forces on the adhesion of the coating to the external surface of a body of revolution during thermal spraying. A mathematical apparatus is proposed for calculating the inertia forces, acting on a particle of coating, applied to the outer surface of the bodies of revolution. As a result, dependencies have been revealed that allow predicting the adhesion strength of the coating with the steel base during thermal spraying.

The Sector Problem

1957 ◽  
Vol 24 (4) ◽  
pp. 574-581
Author(s):  
G. Horvay ◽  
K. L. Hanson
Keyword(s):  
Variational Method ◽  
Orthogonal Polynomials ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Circular Sector ◽  
Orthonormal Polynomials ◽  
Circular Boundary ◽  
Stress Functions ◽  
Complete Set ◽  
Derivatives Of

Abstract On the basis of the variational method, approximate solutions f k ( r ) h k ( θ ) , f k ( r ) g k ( θ ) , F k ( θ ) H k ( r ) , F k ( θ ) G k ( r ) of the biharmonic equation are established for the circular sector with the following properties: The stress functions fkhk create shear tractions on the radial boundaries; the stress functions fkgk create normal tractions on the radial boundaries; the stress functions FkHk create both shear and normal tractions on the circular boundary, and the stress functions FkGk create normal tractions on the circular boundary. The enumerated tractions are the only tractions which these function sets create on the various boundaries of the sector. The factors fk(r) constitute a complete set of orthonormal polynomials in r into which (more exactly, into the derivatives of which) self-equilibrating normal or shear tractions applied to the radial boundaries of the sector may be expanded; the factors Fk(θ) constitute a complete set of orthonormal polynomials in θ into which shear tractions applied to the circular boundary of the sector may be expanded; and the functions Fk″ + Fk constitute a complete set of non-orthogonal polynomials into which normal tractions applied to the circular boundary of the sector may be expanded. Function tables, to facilitate the use of the stress functions, are also presented.

DMRG Approach to Fast Linear Algebra in the TT-Format

2011 ◽  
Vol 11 (3) ◽  
pp. 382-393 ◽  
Author(s):  
Ivan Oseledets
Keyword(s):  
Linear Systems ◽  
Linear Algebra ◽  
Direct Method ◽  
Fast Algorithms ◽  
Approximate Solutions ◽  
Vector Product ◽  
The Matrix ◽  
Minimization Scheme

AbstractIn this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at http://spring.inm.ras.ru/osel

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

A System to Measure Turbulent Lengthscales on Submerged Bodies of Revolution

2017 ◽  
Author(s):  
Christopher J. Chesnakas ◽  
Daniel R. Cadel
Keyword(s):  
Laser Doppler Velocimetry ◽  
Arrival Time ◽  
Noise Removal ◽  
The Body ◽  
Doppler Velocimetry ◽  
Body Of Revolution ◽  
Sampled Data ◽  
Bodies Of Revolution ◽  
Submerged Body ◽  
Cross Correlations

A system has been developed to measure the turbulent lengthscales in the flow about a submerged body of revolution. The system consists of two Laser Doppler Velocimetry (LDV) probes mounted inside the body of revolution with the beams projected outside of the body through conformal windows. The measurement volumes of the two probes can be independently positioned within a plane perpendicular to the body axis. The probes are used to measure velocity time series at various spacings in the flow field. Auto- and cross-correlations are computed for each measurement pair, from which integral lengthscales are then found. Measurements are compared to canonical data from a turbulent free shear jet. In this paper, the system is described and its theory of operation detailed. Methods of computing the velocity correlations from the random-arrival-time LDV measurements are presented, and a new noise-removal scheme for non-uniformly sampled data is introduced. Six methods for calculating the integral lengthscale from autocorrelation data are reviewed, and the results discussed for the present jet data measured with LDV.

A Note on the Resistance of Bodies of Revolution and Ship Forms

1974 ◽  
Vol 18 (03) ◽  
pp. 153-168
Author(s):  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Reasonable Agreement ◽  
The Body ◽  
Experimental Results ◽  
Body Of Revolution ◽  
Bodies Of Revolution ◽  
Boundary Layer Development ◽  
Layer Development

A simple so-called 'equivalent' body of revolution is proposed for reflex ship forms in an attempt to simplify calculation of the boundary layer over a ship's hull when there is no wavemaking. How­ever, exhaustive testing of one body of revolution did not produce a favorable comparison with re­sults for the corresponding reflex model. Gadd's recently proposed theory was used to calculate the boundary-layer development over the body of revolution. Reasonable agreement was obtained between the calculated and experimental results.

Approximate Analytic Method of Piping Systems With Elasto-Plastic Damper

2002 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Simple Procedure ◽  
Continuous System ◽  
Approximate Solutions ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Forced Response ◽  
Mode Shapes ◽  
Piping System ◽  
Restoring Force ◽  
Approximate Methods

An elasto-plastic damper is one of the vibration absorbers in which energy is absorbed by elasto-plastic deformation of the hysteretic type damper. It is used for the piping system. The piping system is continuous system. Since it is difficult to find the analytical solution of the equation of motion for the system with elasto-plastic damper, the equation of motion is treated by various approximate methods in which the system is usually considered as a single- or a multiple-degree-of-freedom system, but not as a continuous system. In order to analyze the response of a nonlinear continuous system, however, it is necessary to consider the system as a continuous system. In this paper, the nonlinear steady-state response of the piping system with elasto-plastic damper is undertaken by approximate solutions, which are easily obtained by a simple procedure and are more practical than the exact solutions. As a continuous model of the piping system, a beam simply supported or clamped at one end, with elasto-plastic damper at the other end is used. The restoring force is modeled as hysteresis loop characteristics in order to consider the energy loss in the damper. In the analysis, the restoring force is expanded into the Fourier series, and only fundamental terms are considered. The resonance curves and mode shapes of the beam are obtained from the approximate solution. And effect of elasto-plastic damper on the forced response of continuous system is examined.

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