Modeling Uncertainty In Three-dimensional Heat
Transfer Problems
Author(s)
X. Wan, D. Xiu & G.E. Karniadakis
Abstract
We present a generalized polynomial chaos method to solve the steady and unsteady
heat transfer problems with uncertainty in boundary conditions, diffusivity
coefficient and forcing terms. The stochastic inputs and outputs are represented
spectrally by employing the orthogonal polynomial functionals from the Askey
scheme, as a generalization of the original polynomial chaos idea of Wiener [1].
A Galerkin projection in random space is applied to derive the equations in weak
form, and a parallel spectral/hp element method is employed to solve the resulting
set of deterministic equations. Simulations in three-dimensional domains with
stochastic dimension 38 and about 150 million unknowns are presented here for
the first time.
Keywords: uncertainty, polynomial chaos, heat conduction.
1 Introduction
Traditionally, heat transfer analy
Keywords
Related Book
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