Accurate macroscale modelling of spatial dynamics in multiple dimensions

Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid microscale dynamics the dynamical systems approach constructs accurate closures of macroscale discretisations of the microscale system. Here we specifically explore reaction-diffusion problems in two spatial dimensions as a prototype of generic systems in multiple dimensions. Our approach unifies into one the modelling of systems by a type of finite elements, and the `equation free' macroscale modelling of microscale simulators efficiently executing only on small patches of the spatial domain. Centre manifold theory ensures that a closed model exist on the macroscale grid, is emergent, and is systematically approximated. Dividing space either into overlapping finite elements or into spatially separated small patches, the specially crafted inter-element/patch coupling also ensures that the constructed discretisations are consistent with the microscale system/PDE to as high an order as desired. Computer algebra handles the considerable algebraic details as seen in the specific application to the Ginzburg--Landau PDE. However, higher order models in multiple dimensions require a mixed numerical and algebraic approach that is also developed. The modelling here may be straightforwardly adapted to a wide class of reaction-diffusion PDEs and lattice equations in multiple space dimensions. When applied to patches of microscopic simulations our coupling conditions promise efficient macroscale simulation.Comment: some figures with 3D interaction when viewed in Acrobat Reader. arXiv admin note: substantial text overlap with arXiv:0904.085

Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

The XDEM Multi-physics and Multi-scale Simulation Technology: Review on DEM-CFD Coupling, Methodology and Engineering Applications

The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an advanced multi- physics simulation technology that combines flexibility and versatility to establish the next generation of multi-physics and multi-scale simulation tools. For this purpose the simulation framework relies on coupling various predictive tools based on both an Eulerian and Lagrangian approach. Eulerian approaches represent the wide field of continuum models while the Lagrange approach is perfectly suited to characterise discrete phases. Thus, continuum models include classical simulation tools such as Computa- tional Fluid Dynamics (CFD) or Finite Element Analysis (FEA) while an ex- tended configuration of the classical Discrete Element Method (DEM) addresses the discrete e.g. particulate phase. Apart from predicting the trajectories of individual particles, XDEM extends the application to estimating the thermo- dynamic state of each particle by advanced and optimised algorithms. The thermodynamic state may include temperature and species distributions due to chemical reaction and external heat sources. Hence, coupling these extended features with either CFD or FEA opens up a wide range of applications as diverse as pharmaceutical industry e.g. drug production, agriculture food and processing industry, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology

Kompetensi pembimbing syarikat bertauliah Sistem Latihan Dual Nasional (SLDN)

Sistem Latihan Dual Nasional (SLDN) merupakan satu sistem latihan dan usahasama antara sektor awam dan sektor swasta dilaksanakan untuk melahirkan tenaga mahir k-worker selari dengan keperluan industri masa kini untuk membangunkan ekonomi negara. Pihak kerajaan dan syarikat swasta menaja pekerja pilihan mereka sebagai pelatih dalam sistem latihan ini bagi mempertingkatkan kebolehan pekerja mereka. Selain itu, pelatih juga terdiri daripada pelajar yang tidak dapat melanjutkan pelajaran ke mana-mana institusi pengajian tinggi awam mahupun swasta. Sistem ini menjalankan pendekatan day release iaitu pelatih menjalani latihan selama empat hari di industri dan satu hari di institusi latihan atau block release iaitu pelatih menjalani latihan kemahiran di industri empat bulan dan satu bulan di institusi latihan mengikut kesesuaian industri tersebut. Kajian berbentuk deskriptif dijalankan untuk melihat melihat tahap kompetensi pembimbing SLDN. Selain itu juga, kajian ini dijalankan bagi melihat perbezaan terhadap tahap pengetahuan, kemahiran dan sikap pembimbing SLDN berdasarkan jantina. Kajian ini juga dibuat bagi menentukan hubungan kompetensi pembimbing berdasarkan pengalaman bekerja. Penyelidikan tinjauan deskriptif ini menggunakan borang soal selidik sebagai instrumen kajian berskala Likert. Seramai 84 orang responden yang terdiri daripada pembimbing syarikat bertauliah SLDN terlibat di dalam kajian ini. Data dianalisis menggunakan SPSS versi 16.0. Hasil analisis mendapati pembimbing mempunyai pengetahuan yang tinggi di samping kemahiran dan sikap. Keputusan inferensi pula menunjukkan tidak terdapat perbezaan antara tahap pengetahuan, kemahiran dan sikap pembimbing berdasarkan jantina manakala analisis korelasi Pearson menunjukkan tidak terdapat hubungan antara kompetensi pembimbing berdasarkan pengalaman bekerja

Kompetensi pembimbing syarikat bertauliah Sistem Latihan Dual Nasional (SLDN)

Sistem Latihan Dual Nasional (SLDN) merupakan satu sistem latihan dan usahasama antara sektor awam dan sektor swasta dilaksanakan untuk melahirkan tenaga mahir k-worker selari dengan keperluan industri masa kini untuk membangunkan ekonomi negara. Pihak kerajaan dan syarikat swasta menaja pekerja pilihan mereka sebagai pelatih dalam sistem latihan ini bagi mempertingkatkan kebolehan pekerja mereka. Selain itu, pelatih juga terdiri daripada pelajar yang tidak dapat melanjutkan pelajaran ke mana-mana institusi pengajian tinggi awam mahupun swasta. Sistem ini menjalankan pendekatan day release iaitu pelatih menjalani latihan selama empat hari di industri dan satu hari di institusi latihan atau block release iaitu pelatih menjalani latihan kemahiran di industri empat bulan dan satu bulan di institusi latihan mengikut kesesuaian industri tersebut. Kajian berbentuk deskriptif dijalankan untuk melihat melihat tahap kompetensi pembimbing SLDN. Selain itu juga, kajian ini dijalankan bagi melihat perbezaan terhadap tahap pengetahuan, kemahiran dan sikap pembimbing SLDN berdasarkan jantina. Kajian ini juga dibuat bagi menentukan hubungan kompetensi pembimbing berdasarkan pengalaman bekerja. Penyelidikan tinjauan deskriptif ini menggunakan borang soal selidik sebagai instrumen kajian berskala Likert. Seramai 84 orang responden yang terdiri daripada pembimbing syarikat bertauliah SLDN terlibat di dalam kajian ini. Data dianalisis menggunakan SPSS versi 16.0. Hasil analisis mendapati pembimbing mempunyai pengetahuan yang tinggi di samping kemahiran dan sikap. Keputusan inferensi pula menunjukkan tidak terdapat perbezaan antara tahap pengetahuan, kemahiran dan sikap pembimbing berdasarkan jantina manakala analisis korelasi Pearson menunjukkan tidak terdapat hubungan antara kompetensi pembimbing berdasarkan pengalaman bekerja