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Keywords:
Low-energy buildings, heat transfer, computational modelling, optimization techniques, MATLAB software tools
Low-energy buildings, heat transfer, computational modelling, optimization techniques, MATLAB software tools
Summary:
European directives and related national technical standards force the substantial reduction of energy consumption of all types of buildings. This can be done thanks to the massive insulation and the improvement of quality of building enclosures, using the simple evaluation assuming the one-dimensional stationary heat conduction. However, recent applications of advanced materials, structures and technologies force the proper physical, mathematical and computational analysis coming from the thermodynamic principles. This paper shows the non-expensive evaluation of energy consumption of buildings with controlled indoor temperature, decomposing a building, considered as a thermal system, into particular subsystems and elements, coupled by interface thermal fluxes. We come to a rather large parabolic system of partial differential equations, containing the nonlinearities i) from the surface Stefan - Boltzmann radiation and ii) from the heating control; this can be handled using some properties of semilinear systems. The Fourier multiplicative decomposition together with the finite element technique enables us to derive a sparse system of ordinary differential equations, appropriate for the input of climatic data (temperature, beam and diffuse solar radiation). For the approximate solutions the spectral analysis is helpful; all nonlinearities can be overcome thanks to quasi-Newton iterations. All above sketched simulations have been implemented in MATLAB. An example shows the validation of this approach, utilizing the time series of measured energy consumption from the real family house in Ostrov u Macochy (30 km northern from Brno). Additional procedures for the support of design of low-energy buildings come namely from the Nelder - Mead optimization algorithm.
References:
[1] Castro, A. Bermúdez de: Continuum Thermodynamics. Birkh\"auser, Basel, 2005.
[2] Borwein, J., Lewis, A.: Convex Analysis and Nonlinear Optimization. Springer, New York, 2006. MR 2184742
[3] Brigola, R.: Fourier-Analysis und Distributionen. (in German), Co-Verlag, Berlin, 2012.
[4] Carluci, S., Pagliano, L.: A review of indices for the long-term evaluation of the general thermal comfort conditions in buildings. Energy and Buildings, 53 (2012), pp. 194–205. DOI 10.1016/j.enbuild.2012.06.015
[5] Crawley, D. B.: Contrasting the capabilities of building energy performance simulation programs. Building and Environment, 43 (2008), pp. 661–673. DOI 10.1016/j.buildenv.2006.10.027
[6] Davies, M. G.: Building Heat Transfer. J. Wiley & Sons, Chichester, 2004.
[7] Drábek, P., Milota, J.: Lectures on Nolinear Analysis. University of West Bohemia, Pilsen, 2004.
[8] Feist, W.: Gestaltungsgrundlagen Passivh\"auser. (in German), Das Beispiel, Darmstadt, 1999.
[9] Feist, W., Pfluger, R., Kaufmann, B., Schnieders, J., Kah, O.: Passive House Planning Package. Passive House Institute, Darmstadt, 2004.
[10] Gao, F., Han, L.: Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Computer Optimizations and Applications, 99 (2010), pp. 111–222. MR 2872499
[11] Hudec, M., Johanisová, B., Mansbart, T.: Pasivní domy z přírodních materiálů. (in Czech), Grada, Prague, 2012.
[12] Jarošová, P.: Computational approaches to the design of low-energy buildings. Programs and Algorithms of Numerical Mathematics in Dolní Maxov (Czech Republic), Proceedings, 2014, pp. 92–99, Institute of Mathematics AS CR, Prague, 2015.
[13] Jarošová, P., Vala, J.: On a computational model of building thermal dynamic response. Thermophysics in Terchová (Slovak Republic), Proceedings, 2016, pp. 40011/1–6, American Institute of Physics, Melville (USA), 2016.
[14] Jarošová, P., Vala, J.: Optimization approaches in the thermal system analysis of buildings. ICNAAM (International Conference on Numerical Analysis and Applied Mathematics) in Thessaloniki, Proceedings, 2017, 4 pp., American Institute of Physics, Melville (USA),2018, accepted for publication.
[15] Kämpf, J. H., Robinson, D. A.: A simplified thermal model to support analysis of urban resource flows. Energy and Buildings, 39 (2007), pp. 445–453. DOI 10.1016/j.enbuild.2006.09.002
[16] Lagarias, J. C., Reeds, J. A., Wrigth, M. H., Wrigth, P. E.: Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM Journal of Optimization, 9 (1998), pp. 112–147. DOI 10.1137/S1052623496303470 | MR 1662563
[17] Lagarias, J. C., Poonen, B., Wrigth, M. H.: Convergence of the restricted Nelder-Mead algorithm in two dimensions. SIAM Journal on Optimization, 22 (2012), pp. 501–532. DOI 10.1137/110830150 | MR 2968864
[18] Maz’ya, V. G.: Sobolev Spaces with Applications to Elliptic Partial Differential Equations. Springer, Berlin, 2011. MR 2777530
[19] Nelder, J. A., Mead, R.: Simplex method for function minimization. Computer Journal, 7(1965), pp. 308–313. DOI 10.1093/comjnl/7.4.308 | MR 3363409
[20] Roubíček, T.: Nonlinear Partial Differential Equations with Applications. Birkh\"auser, Basel, 2005. MR 2176645
[21] Řehánek, J.: Tepelná akumulace budov. (in Czech), ČKAIT, Prague, 2002.
[22] Shukuya, M.: Exergy – Theory and Applications in the Built Environment. Springer, London, 2013.
[23] Šťastník, S., Vala, J.: On the thermal stability in dwelling structures. Building Research Journal, 52 (2004), pp. 31–55.
[24] Underwood, J. C.: An improved lumped parameter method for building thermal modelling. Energy and Buildings, 79 (2014), pp. 191–201. DOI 10.1016/j.enbuild.2014.05.001
[25] Viggers, H., Keall, M., Wickens, K., Howden-Chapman, P.: Increased house size can cancel out the effect of improved insulation on overall heating energy requirements. Energy Policy 107 (2017), pp. 248–257. DOI 10.1016/j.enpol.2017.04.045
[26] Wright, M. H., Nelder,: Mead, and the other simplex method. Documenta Mathematica, extra volume Optimization Stories (2012), pp. 271–276. MR 2991490
[27] Ženíšek, A.: Finite element variational crimes in parabolic-elliptic problems. Numerische Mathematik, 55 (1989), pp. 343–376. DOI 10.1007/BF01390058 | MR 0993476
[28] Ženíšek, A.: Sobolev Spaces and Their Applications in the Finite Element Method. Brno University of Technology, 2005.
[29] HASH(0x191cb68): [29] Directive 2010/31/EU of the European Parliament and of the Council on the Energy Performance of Buildings, Official Journal of the European Union, L 153/13 (2010).
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