Least Squares Differential Quadrature Time
Integration Scheme In The Dual Reciprocity
Boundary Element Method Solution Of
Convection-diffusion Problems
Author(s)
C. Bozkaya
Abstract
The least squares differential quadrature method (DQM) is used for solving the
ordinary differential equations in time, obtained from the application of the dual
reciprocity boundary element method (DRBEM) for the spatial partial derivatives
in convection-diffusion type problems. The DRBEM enables us to use the fundamental
solution of the Laplace equation which is easy to implement computationally.
The time derivative and the convection terms are considered as the nonhomogeneity
in the equation which are approximated in terms of radial basis functions.
The application of DQM for time derivative discretization when it is combined
with the DRBEM gives an overdetermined system of linear equations since both
boundary and initial conditions are imposed. Then the least squares approximation
is made use of for solving the overdetermined system. Thus, the solution is
obtained at any time level without an iterative scheme. Numerical results are in
very good agreementwith the theoretical solutions of the test problems considered.
Keywords: dual reciprocity boundary element method, differential quadrature
method, convection–diffusion equation.
1 Introduction
The numerical solution of transient convection-diffusion problems is a challenging
task because of the occurrence of these equations in many branches of science
and engineering. Solving time dependent problems, classical methods discretize
the spatial domain of the problem with one of the known methods such as finite
Keywords
dual reciprocity boundary element method, differential quadrature
method, convection–diffusion equation
Related Book
Other papers in this volume
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