Numerical simulation for unsteady anisotropic-diffusion convection equation of spatially variable coefficients and incompressible flow
Main Article Content
Abstract
The anisotropic-diffusion convection equation of spatially
variable coefficients which is relevant for functionally graded media
is discussed in this paper to find numerical solutions by using a
combined Laplace transform and boundary element method. The variable
coefficients equation is transformed to a constant coefficients equation.
The constant coefficients equation is then Laplace-transformed so
that the time variable vanishes. The Laplace-transformed equation
is consequently written in a pure boundary integral equation which
involves a time-free fundamental solution. The boundary integral equation
is therefore employed to find numerical solutions using a standard
boundary element method. Finally the results obtained are inversely
transformed numerically using the Stehfest formula to get solutions
in the time variable. The combined Laplace transform and boundary
element method is easy to be implemented, efficient and accurate for
solving unsteady problems of anisotropic functionally graded media
governed by the diffusion convection equation.
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