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©2012 Civil-Comp Ltd |
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J. Kruis, T. Krejcí, J. Sýkora and M. Šejnoha
Department of Mechanics, Czech Technical University in Prague, Czech Republic
Keywords: coupled heat and moisture transport, Künzel model, parallel computing.
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reference
The coupled heat and moisture transport is required in connection with analyses of
historical buildings and structures which are usually made of masonry. Detailed
models of bricks and plaster can be used only for analyses of small segments of
masonry structures. If the whole masonry structure has to be analysed, a suitable
homogenization technique has to be used because of the strong material heterogeneity.
The classical first order homogenization in a spatial domain in the framework
of the two-step multiscale computational scheme was proposed in [1]. A significant
dependence of the homogenized properties on actual moisture gradients and
corresponding values of both macroscopic temperature and relative humidity
was observed.
The Künzel material model [2] of coupled heat and moisture transport was selected
for both levels of the analysis. The model is based on the mass and heat
balance equations where the temperature and relative humidity are unknown
functions. The finite elements in the analysis on the macro-level, which is also
called the macro-problem, use the matrices
of material parameters which are obtained from the
homogenization. It means that the appropriate material matrices are assembled as a result
of solution of the corresponding meso-level problems. The enormous
computational demand stems from the fact that the material matrix
has to be determined for each integration point in the macro-problem.
If a standard mesh with thousands or tens of thousands of finite elements
is used on the macro-problem, the number of integration points is in the order of
tens or hundreds of thousands. Therefore, the meso-level problem
has to be solved many times. Although the meso-level problem
usually contains only hundreds of elements, the computational
requirements are huge.
Fortunately, the solution of many meso-level problems is an excellent
example of computation suitable for processor farming [3]. The master
processor executes the macro-problem while all other processors,
called the slave processors, deal with meso-level problems. The master
sends to each slave only the actual temperature, relative humidity
and their gradients (8 values in total). On the other hand, the slaves
send to the master the material matrix and the coefficient of capacity
(40 values in total).
The access to a parallel computer with thousands of processors is not common.
Therefore, several meso-level problems are assigned to each slave which
leads to the significantly reduced number of processors needed.
From the physical point of view, it is also acceptable to use
homogenized material parameters in more than one integration point
of the macro-problem. Clearly, the material matrices do not change
dramatically in the nearby integration points in the macro-problem.
First order homogenization in a spatial domain in the framework
of the two-step multiscale computational scheme is applied
to real world problems in two and three spatial dimensions. Analyses
are performed on a cluster of PC.
- 1
- J. Sýkora, M. Šejnoha, J. Šejnoha, "Homogenization of coupled heat and moisture transport in masonry structures including interfaces", Applied Mathematics and Computation, 2011. doi: 10.1016/j.amc.2011.02.050
- 2
- H.M. Künzel, "Simultaneous Heat and Moisture Transport in Building Components", Fraunhofer Institute of Building Physics, Fraunhofer IRB Verlag Stutgart, 1995.
- 3
- B.H.V. Topping, A.I. Khan, "Parallel Finite Element Computations", Saxe-Coburg Publications, Edinburgh, UK, 1996.
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