A mathematical model and numerical solution of interface problems for steady state heat conduction

Z. Muradoglu Seyidmamedov and Ebru Ozbilge

Mathematical Problems in Engineering, 2006, vol. 2006, 1-18

Abstract:

We study interface (or transmission) problems arising in the steady state heat conduction for layered medium. These problems are related to the elliptic equation of the form A u : = − ∇ ( k ( x ) ∇ u ( x ) ) = F ( x ) , x ∈ Ω ⊂ ℝ 2 , with discontinuous coefficient k = k ( x ) . We analyse two types of jump (or contact) conditions across the interfaces Γ δ − = Ω 1 ∩ Ω δ and Γ δ + = Ω δ ∩ Ω 2 of the layered medium Ω : = Ω 1 ∪ Ω δ ∪ Ω 2 . An asymptotic analysis of the interface problem is derived for the case when the thickness ( 2 δ > 0 ) of the layer (isolation) Ω δ tends to zero. For each case, the local truncation errors of the used conservative finite difference scheme are estimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficient k = k ( x ) . The presented numerical results illustrate high accuracy and show applicability of the given approach.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:020898

DOI: 10.1155/MPE/2006/20898

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