A numerical approximation of the thermal coupling of fluids and solids

In this article we analyze the problem of the thermal coupling of fluids and solids through a common interface. We state the global thermal problem in the whole domain, including the fluid part and the solid part. This global thermal problem presents discontinuous physical properties that depend on the solution of auxiliary problems on each part of the domain (a fluid flow problem and a solid state problem). We present a domain decomposition strategy to iteratively solve problems posed in both subdomains and discuss some implementation aspects of the algorithm. This domain decomposition framework is also used to revisit the use of wall function approaches used in this context. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  R. Codina,et al.  Time dependent subscales in the stabilized finite element approximation of incompressible flow problems , 2007 .

[2]  Yousef Saad,et al.  ILUT: A dual threshold incomplete LU factorization , 1994, Numer. Linear Algebra Appl..

[3]  Michael B. Giles,et al.  Stability analysis of numerical interface conditions in fluid-structure thermal analysis , 1997 .

[4]  Bernhard A. Schrefler,et al.  Simulation of damage-permeability coupling in hygro-thermo mechanical analysis of concrete at high temperature , 2002 .

[5]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[6]  C. Jayatilleke,et al.  The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer , 1966 .

[7]  Ramon Codina,et al.  Dynamic subscales in the finite element approximation of thermally coupled incompressible flows , 2007 .

[8]  Guillaume Houzeaux,et al.  A Geometrical Domain Decomposition Methods in Computational Fluid Dynamics , 2002 .

[9]  R. Codina,et al.  A stabilized finite element approximation of low speed thermally coupled flows , 2008 .

[10]  R. Codina.  Stabilized finite element approximation of transient incompressible flows using orthogonal subscales , 2002 .

[11]  P. Sagaut.  Large Eddy Simulation for Incompressible Flows , 2001 .

[12]  Eliseo Chacón Vera,et al.  Study of a non-overlapping domain decomposition method: poisson and stokes problems , 2004 .

[13]  A. Abdel-azim.  Fundamentals of Heat and Mass Transfer , 2011 .

[14]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[15]  Guillaume Houzeaux,et al.  Numerical approximation of the heat transfer between domains separated by thin walls , 2006 .

[16]  Philippe H. Geubelle,et al.  Stability of fluid–structure thermal simulations on moving grids , 2007 .