scholarly journals Non-singular boundary integral methods for fluid mechanics applications

2012 ◽  
Vol 696 ◽  
pp. 468-478 ◽  
Author(s):  
Evert Klaseboer ◽  
Qiang Sun ◽  
Derek Y. C. Chan
Keyword(s):  
Stokes Flow ◽  
Integral Method ◽  
Practical Interest ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Singular Boundary ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Weakly Singular ◽  
Principal Value

AbstractA formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad applicability of the approach is illustrated with a number of problems of practical interest to fluid and continuum mechanics including the solution of the Laplace equation for potential flow, the Helmholtz equation as well as the equations for Stokes flow and linear elasticity.

Boundary Integral Methods for Thermoelasticity Problems

1986 ◽  
Vol 53 (2) ◽  
pp. 298-302 ◽  
Author(s):  
S. Sharp ◽  
S. L. Crouch
Keyword(s):  
Heat Flow ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Thermally Induced ◽  
Flow Problems ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Transient Heat Flow ◽  
Induced Stresses

The boundary integral method for solving transient heat flow problems is extended to calculate thermally induced stresses and displacements. These results are then corrected by means of an elastostatic solution to satisfy the boundary conditions.

scholarly journals Springs, Formulas and Flatland:A Path to Boundary Integral Methods in Elasticity

2007 ◽  
Vol 1 (1) ◽  
Author(s):  
Frank J. Rizzo
Keyword(s):  
Boundary Value Problems ◽  
Computational Methods ◽  
Integral Method ◽  
Early Period ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Research Experience ◽  
Boundary Integral Methods ◽  
Long Period ◽  
Integral Methods

This memoir is about some embryonic thoughts and experiences with what is now often called the Direct Boundary Integral Method for boundary value problems in ‘classical elastostatics.’ It covers a very early period for me, from about 1954 to 1965, when I wrestled with relevant theoretical and mathematical issues, which I thought were important, primarily in the last two or three of those years. This was before I became aware of other contributors to the method, who are not mentioned here, and before they became aware of my work. So this is not a memoir largely filled with recollections of people and places; although I believe that subsequent interactions with fellow contributors and users of computational methods have become the most important part of my research experience. In any case, I understand that memoirs and papers of a more technical nature, written by some of those contributors, are part of these EJBE volumes. Those writings have bearing, no doubt, on the present memoir and much more, over a long period of time, and I look forward to reading them all....

Virtual Boundary Integral Method for Anisotropic Potential Problems

2012 ◽  
Vol 155-156 ◽  
pp. 370-374
Author(s):  
Xin Rong Jiang ◽  
Xin Fu
Keyword(s):  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Singular Boundary ◽  
Boundary Integrals ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Potential Problems ◽  
Virtual Boundary ◽  
Virtual Boundary Element

Heat conduction in anisotropic materials has important applications in science and engineering. In this paper the virtual boundary element method (VBEM) is applied to solve these problems. Due to the fact of a virtual boundary outside the real boundary, the VBEM does not need to treat the singular boundary integrals, and thus, is more accurate and convenient than the traditional one. Numerical examples are presented, to demonstrate the efficiency and accuracy of this method.

scholarly journals A General Algorithm of the Boundary Integral Method for Solving Laplace’s Mixed Boundary Value Problem

2021 ◽  
pp. 71-85
Author(s):  
Rajesh Kumar Pal ◽  
Pradeep Kothiyal ◽  
Deependra Nigam
Keyword(s):  
Integral Method ◽  
Mixed Boundary ◽  
Practical Interest ◽  
Boundary Elements ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
General Algorithm ◽  
Boundary Problems ◽  
Mixed Boundary Problems ◽  
Good Agreement

Boundary elements have emerged as a powerful alternative to finite elements particularly in cases where better accuracy is required. The most important features of boundary elements however is that it only requires descretization of the surface rather than the volume. Here, A general algorithm of the boundary integral method has been formulated for solving elliptic partial differential equations. The broad applicability of the approach is illustrated with a problem of practical interest giving the solution of the Laplace equation for potential flow with mixed boundary problems. The results and patterns are shown in tables and figures and compared well with Brebbia [1] are found in good agreement.

scholarly journals An indirect boundary integral method for an oscillatory Stokes flow problem

2003 ◽  
Vol 2003 (47) ◽  
pp. 2961-2976 ◽  
Author(s):  
Mirela Kohr
Keyword(s):  
Newtonian Fluid ◽  
Stokes Flow ◽  
Integral Method ◽  
Flow Problem ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Rigid Spheres ◽  
Incompressible Newtonian Fluid

The purpose of this paper is to present an indirect boundary integral method for the oscillatory Stokes flow provided by the translational oscillations of two rigid spheres in an incompressible Newtonian fluid of infinite expanse.

scholarly journals Compressible bubbles in Stokes flow

2003 ◽  
Vol 476 ◽  
pp. 345-356 ◽  
Author(s):  
DARREN G. CROWDY
Keyword(s):  
Stokes Flow ◽  
Boundary Integral ◽  
Nonlinear Ordinary Differential Equations ◽  
Shape Evolution ◽  
Initial Condition ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Finite Set ◽  
The Relationship ◽  
Compressible Bubble

The problem of a two-dimensional inviscid compressible bubble evolving in Stokes flow is considered. By generalizing the work of Tanveer & Vasconcelos (1995) it is shown that for certain classes of initial condition the quasi-steady free boundary problem for the bubble shape evolution is reducible to a finite set of coupled nonlinear ordinary differential equations, the form of which depends on the equation of state governing the relationship between the bubble pressure and its area. Recent numerical calculations by Pozrikidis (2001) using boundary integral methods are retrieved and extended. If the ambient pressures are small enough, it is shown that bubbles can expand significantly. It is also shown that a bubble evolving adiabatically is less likely to expand than an isothermal bubble.

Sign in / Sign up

Export Citation Format

Share Document