Residual-free Bubble Shape Functions Used In
BEM For The Stability Of The Solution Of The
Convective-diffusion Transport Equation
Author(s)
P. Kocutar, L. ˇSkerget & J. Ravnik
Abstract
In this paper we focus on oscillation and instability of the solution of the
convective-diffusive equation depending on the Peclet number. For that purpose,
different types of mesh elements and shape functions have been used. For the
stabilization of the solution of the convective-diffusive equation for high Peclet
numbers, we employed high-order polynomial shape functions, namely residualfree
bubble functions. The numerical scheme is based on BEM. For solving
the linear homogeneous part of the partial differential equation, the Laplace
fundamental solution has been used.
We compared quadratic nine-node domain element using Lagrangian shape
functions, linear four-node domain element using Lagrangian shape functions and
linear four-node domain element using fourth-order bubble enriched functions.
Numerical results obtained with linear Lagrangian shape function and bubble
enriched functions are compared with the analytical solution.
Residual-free bubble functions add stability to simulation and despite the fact
that less nodes are used in the domain element, the results are comparable and
in some cases even better than the quadratic nine-node domain element. The
boundary element method with usage of bubble-enriched functions can resolve
problems of convective-diffusion and obtain stable and accurate solutions for this
type of governing equations, which are being represented in several types of
transport phenomena.
Keywords: boundary element method, residual free bubble, upwinding techniques,
convective-diffusion equation.
Keywords
boundary element method, residual free bubble, upwinding techniques,
convective-diffusion equation.
Related Book
Other papers in this volume
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