Program
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Thursday Aug 11, 2005
1:30 PM to 5:00 PM
Instructors:
Alain J. Kassab, Mechanical, Materials and Aerospace Engineering, UCF
Eduardo Divo, Department of Engineering Technology, UCF
TOPICS:
- Introduction: Relation of the BEM to Green's function method, Green's
free space solutions, boundary integral equation formulation for potential
problems and elasticity, integral equation formulation by method of
weighted residuals.
- Potential problems: theoretical formulation, computational aspects, and
detailed solution of a constant element example. Solution of potential
problems with linear, quadratic, and cubic elements.
- Addressing corner problems: double nodes, discontinuous elements, and
other formulations.
- Poisson's equation: addressing generation. Computing domain integrals,
particular solutions, and point sources/sinks. Transforming domain into
boundary integrals: particular solutions, multiple reciprocity method, and
dual reciprocity method. Application of the Monte Carlo method.
- Steady heat conduction: nonlinear boundary conditions, variable thermal
conductivity, anisotropy, and regional inhomogenieties.
- Transient BEM: transient fundamental solutions with constant and
linear elements, Laplace transform methods and numerical inversion of
the Laplace transform solution, finite difference hybrid methods, and
dual reciprocity applications.
- Dealing with inhomogeneous media, generalized BEM in inhomogeneous
media (media in which material properties vary with position): isotropic
and anisotropic formulation using a generalized non-symmetric singular
forcing function and generalized fundamental solution
- Further applications: steady and transient heat conduction in thin plates, axisymmetric BEM, DRBEM for fluid flow, BEM for infinite and semi-infinite extent, indirect boundary element methods.
- Three dimensional BEM, domain decomposition and parallel computation. Introduction to multipole methods.
- Application to conjugate heat transfer: coupling BEM heat conduction solver and FVM Navier-Stokes solver.
- Introduction to meshless radial basis function method of Kansa and development for heat conduction.
- Extension of the meshless method to Navier-Stokes equations and the pressure correction scheme. Development of domain decomposition and implementation on a parallel platform.
REFERENCES:
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Divo, E. and Kassab, A.J., Boundary Element Method for Heat Conduction with Applications in
NonHomogeneous Media, Wessex Institute of Technology (WIT) Press, Southampton, UK, and
Boston, USA, 2003.
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Wrobel, L.C. The Boundary Element Methods - applications to thermofluids and acoustics, McGraw Hill
Book Co., New York, 2002.
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Brebbia, C.A. and Dominguez, J., Boundary Elements: an introductory course, McGraw-Hill Book
Company, New York, 1992.
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Brebbia, C.A., Telles, J.C.F., and Wrobel, L.C., Boundary Element Techniques in Engineering, Springer-Verlag, New York, 1984.
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