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Boundary Integral Method (boundary + integral_method)
Selected AbstractsBoundary integral method for Stokes flow past a porous bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Mirela Kohr Abstract In this paper we obtain an indirect boundary integral method in order to prove existence and uniqueness of the classical solution to a boundary value problem for the Stokes,Brinkman-coupled system, which describes an unbounded Stokes flow past a porous body in terms of Brinkman's model. Therefore, one assumes that the flow inside the body is governed by the continuity and Brinkman equations. Some asymptotic results in both cases of large and, respectively, of low permeability are also obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] A Galerkin boundary integral method for multiple circular elastic inclusionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001S. G. Mogilevskaya Abstract The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss,Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Christopher P. Kent Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Boundary integral method for Stokes flow past a porous bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Mirela Kohr Abstract In this paper we obtain an indirect boundary integral method in order to prove existence and uniqueness of the classical solution to a boundary value problem for the Stokes,Brinkman-coupled system, which describes an unbounded Stokes flow past a porous body in terms of Brinkman's model. Therefore, one assumes that the flow inside the body is governed by the continuity and Brinkman equations. Some asymptotic results in both cases of large and, respectively, of low permeability are also obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low-frequency theoryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2002C. Athanasiadis Abstract The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far-field patterns are derived. A low-frequency theory for the approximation of the solution to the above problem, and the derivation of the far-field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical analysis of a non-singular boundary integral method: Part II: The general caseMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2002P. Dreyfuss In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we have presented in a previous paper a method which consists in inverting, on a finite element space, a non-singular integral operator for circular domains. This operator was described as a geometrical perturbation of the Steklov operator, and we have precisely defined the relation between the geometrical perturbation and the dimension of the finite element space, in order to obtain a stable and convergent scheme in which there are non-singular integrals. We have also presented another point of view under which the method can be considered as a special quadrature formula method for the standard piecewise linear Galerkin approximation of the weakly singular single-layer potential. In the present paper, we extend the results given in the previous paper to more general cases for which the Laplace problem is set on any ,,, domains. We prove that the properties of stability and convergence remain valid. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical solution of thermal convection problems using the multidomain boundary element methodNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2002W. F. Florez Abstract The multidomain dual reciprocity method (MD-DRM) has been effectively applied to the solution of two-dimensional thermal convection problems where the momentum and energy equations govern the motion of a viscous fluid. In the proposed boundary integral method the domain integrals are transformed into equivalent boundary integrals by the dual reciprocity approach applied in a subdomain basis. On each subregion or domain element the integral representation formulas for the velocity and temperature are applied and discretised using linear continuous boundary elements, and the equations from adjacent subregions are matched by additional continuity conditions. Some examples showing the accuracy, the efficiency and flexibility of the proposed method are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 469,489, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10016 [source] Numerical simulation of non-viscous liquid pinch off using a coupled level set boundary integral methodPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Maria Garzon The pinch off of an inviscid fluid column is described using a potential flow model with capillary forces. The interface velocity is obtained via a Galerkin boundary integral method for the 3D axisymmetric Laplace equation, whereas the interface location and the velocity potential on the free boundary are both approximated using level set techniques on a fixed domain. The algorithm is validated computing the Raleigh-Taylor instability for liquid columns which provides an analytical solution for short times. The simulations show the time evolution of the fluid tube and the algorithm is capable of handling pinch-off and after pinch-off events. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||