Three-dimensional unsteady transonic flow: An integral equation formulation

1987 ◽  
Vol 2 (4) ◽  
pp. 268-270
Author(s):  
J. A. Gear
Keyword(s):  
Integral Equation ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Equation Formulation ◽  
Integral Equation Formulation

A well-posed integral equation formulation for three-dimensional rough surface scattering

2006 ◽  
Vol 462 (2076) ◽  
pp. 3683-3705 ◽  
Author(s):  
Simon N Chandler-Wilde ◽  
Eric Heinemeyer ◽  
Roland Potthast
Keyword(s):  
Integral Equation ◽  
Rough Surface ◽  
Double Layer ◽  
Inverse Operator ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Wave Number ◽  
Layer Potential ◽  
Equation Formulation ◽  
Integral Equation Formulation

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage–Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space when the scattering surface does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, κ , for κ >0, if the coupling parameter η is chosen proportional to the wave number. In the case when is a plane, we show that the choice is nearly optimal in terms of minimizing the condition number.

Integral equation formulation for transonic flow past lifting wings

AIAA Journal ◽  
1978 ◽  
Vol 16 (9) ◽  
pp. 1015-1016 ◽  
Author(s):  
Sunil Kumar Chakrabartty
Keyword(s):  
Integral Equation ◽  
Transonic Flow ◽  
Equation Formulation ◽  
Flow Past ◽  
Integral Equation Formulation

An Integral-Equation Formulation for Anisotropic Elastostatics

1996 ◽  
Vol 63 (4) ◽  
pp. 891-902 ◽  
Author(s):  
M. M. Perez ◽  
L. C. Wrobel
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Structural Elements ◽  
Equation Formulation ◽  
Direct Extension ◽  
Integral Equation Formulation ◽  
Linear Elastostatics ◽  
Anisotropic Problems ◽  
Shear Effects ◽  
Domain Term

In this paper a conceptually simple integral-equation formulation for homogeneous anisotropic linear elastostatics is presented. The basic idea of the approach proposed here is to rewrite the system of differential equations of the anisotropic problem to enable the use of the isotropic fundamental solution. This procedure leads to an extended form of Somigliana’s identity where a domain term occurs as a result of the anisotropy of the material. A supplementary integral equation is then established to cope with the resulting domain unknowns. Although the solution of these integral equations requires discretization of the contour of the structural component into boundary elements and its domain into internal cells, the numerical scheme presented here depends only on the boundary variables of the problem. Once the boundary solution is obtained it is possible to compute the unknowns within the domain, if required. The main objective of the present work is to develop an alternative integral-equation formulation that could be used to reduce the time needed to compute three-dimensional solutions for linear homogeneous anisotropic problems. Another possible advantage of the proposed formulation is its generality, which enables its direct extension to include dynamic and plastic effects in the analysis. Encouraging results are presented for four examples where structural elements are submitted to tension and shear effects.

Modeling three-dimensional scatterers using a coupled finite element-integral equation formulation

1996 ◽  
Vol 44 (4) ◽  
pp. 453-459 ◽  
Author(s):  
T. Cwik ◽  
C. Zuffada ◽  
V. Jamnejad
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Three Dimensional ◽  
Equation Formulation ◽  
Integral Equation Formulation
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