In recent years, Trefftz methods have received increasing attention, as being alternatives of the already well-established element-based simulation methods (e.g., finite element and boundary element methods). The wave-based technique is based on the indirect Trefftz approach for the solution of steady-state, time-harmonic acoustic problems. The dynamic field variables are expanded in terms of wave functions, which satisfy the governing partial differential equation, but do not necessarily satisfy the imposed boundary conditions. Therefore, the approximation error of the method is exclusively caused by the error on the boundary, since there is no additional error present in the domain. The authors investigate the potentials of a novel boundary
error indicator-controlled adaptive local refinement strategy. Practical, industrial-oriented application of the method is presented on the 3D free-field sound radiation model of a simplified combustion engine. Results and efficiency of the approach are compared to a priori, frequency-dependent global refinement strategies.

*Keywords:* Trefftz method, adaptivity, error indicator, boundary error, Wave Based Technique, engine sound, numerical acoustics.

Yusuke Asakuma, Masahiro Asada, Yushin Kanazawa, Tsuyoshi Yamamoto. Anisotropy of effective thermal conductivity analysis of heat transfer coefficient distribution around spherical particles in a packed bed. CAMES 2015 (22)

Effective thermal conductivity with radiation is analyzed by a homogenization method. The method used can precisely represent the conditions around particles in a packed bed. In this study, the effects of variation in parameters such as heat transfer coefficient distribution around spherical particles in a packed bed, Reynolds number, temperature and particle size on the conductivity were estimated in order to elucidate the heat transfer mechanism of complex packed structures. The results show that it is unnecessary in
heat transfer analysis to consider the anisotropic behavior of the flow direction for larger particles, high Reynolds numbers and high temperatures. However, the heat transfer was anisotropic for smaller particle sizes.

*Keywords:* effective thermal conductivity homogenization method, multi-scale analysis microstructure, thermal radiation, packed bed.

Aleksander Marek, Tomasz Garbowski. Homogenization of sandwich panels. CAMES 2015 (22)

The numerical modeling of plates with periodic corrugation requires some efforts to be made in terms of careful and precise discretization of the complicated structure. This automatically generates very computationally expensive models. One of the most popular methods of model simplification is analytical or numerical homogenization. The main goal of this paper is to present the homogenization techniques that can be used to effectively model sandwich panels such as corrugated plates in an elastic phase. Two methods of different complexity are described: homogenization through application of the classical laminated plate theory and homogenization through the deformation energy-equivalence method. The accuracy of these methods is compared with the literature data and the results of a structural sample in two basic tests, i.e., the four-point bending test and the uniaxial tensile test. The results show that each method provides similar effective parameters which proves the robustness of the presented methods.

*Keywords:* homogenization, finite element method, corrugated cardboard.

Eisuke Kita, Wataru Nanya, Yukiko Wakita, Tatsuhiro Tamaki. Traffic network design by cellular automaton-based traffic simulator. CAMES 2015 (22)

Braess pointed out that adding a new road to overcome a traffic congestion could cause a new traffic congestion leading to the reduction of the traffic flow in the whole traffic network, which is called Braess' paradox. The aim of this study is to formulate a traffic network design algorithm to increase the traffic flow in a traffic network. The objective function is the traffic flow of the whole traffic network and the route selection at the corners is considered as design variable. The traffic flow is estimated by a traffic flow
simulator based on the cellular automaton model. A simple traffic network is considered as a numerical example. At different traffic densities, the traffic network is optimized to maximize the traffic flow. The results show that the optimized traffic network depends on traffic density. The situation presented by Braess' paradox could disappear at high traffic density.

*Keywords:* traffic network design, cellular automaton, optimization, Braess' paradox.

Fabio Dall Cortivo, Ezzat S. Chalhoub, Haroldo F. Campos Velho, Milton Kampel. Chlorophyll profile estimation in ocean waters by a set of artificial neural networks. CAMES 2015 (22)

In this work, we propose a methodology to estimate the profile of chlorophyll concentration from the upwelling radiation at the ocean surface, using a system of artificial neural networks (ANNs). The input patterns to train the networks are obtained from the resolution of the radiative transfer equation, where the absorption and scattering coefficients are represented by bio-optical models, with the profile of chlorophyll concentrations based on a shifted-Gaussian model. In the performed analysis, we used 14 720 profiles of chlorophyll that were generated by attributing two values to the biomass quantity, and by considering two sets of wavelengths and three sets containing the directions in which the radiation emitted at the surface is measured. To be able to recover the chlorophyll profile, we need to use a system of networks that works in a "cascade mode". The first one performs an analysis on the features of the chlorophyll profile from the upwelling radiation and determines which profiles can be recovered. The second and third ANNs act only on those profiles that can be recovered. The second ANN performs estimation of the standard deviation from the upwelling radiation and the chlorophyll concentration at the surface. Finally, the third ANN performs an estimation of the peak depth from the upwelling radiation, the chlorophyll concentration at the surface and the standard deviation estimated by second network. The stopping criteria we adopted was
the cross-validation process. The obtained results show that the proposed methodology is quite promising.

*Keywords:* radiative transfer equation, inverse problems, artificial neural networks, chlorophyll profile concentration, bio-optics, phytoplankton.

IACM and ECCOMAS. 2015- Announcements. CAMES 2015 (22)

ECCOMAS. 2015- Announcements. CAMES 2015 (22)

PCM and CCM. PCM-CMM- 2015 CONGRESS. CAMES 2015 (22)

CISM. Programme 2015. CAMES 2015 (22)

Polish Academy of Sciences and Institute of Fundamental Technological Research. Journals and Books. CAMES 2015 (22)