EU Regional School - Persson Seminar
Prof. Dr. Per-Olof Persson - High-Order Discontinuous Galerkin Methods for Fluid and Solid Mechanics
Department of Mathematics
University of California at Berkeley, USA
It is widely believed that high-order accurate numerical methods, for example discontinuous Galerkin (DG) methods, will eventually replace the traditional low-order methods in the solution of many problems, including fluid flow, solid dynamics, and wave propagation. The lecture will give an overview of this field, including the theoretical background of the numerical schemes, the efficient implementation of the methods, and examples of real-world applications. Topics include high-order compact and sparse numerical schemes, high-quality unstructured curved mesh generation, scalable preconditioners for parallel iterative solvers, fully discrete adjoint methods for PDE-constrained optimization, and implicit-explicit schemes for the partitioning of coupled fluid-structure interaction problems. The methods will be demonstrated on some important practical problems, including the inverse design of energetically optimal flapping wings and large eddy simulation (LES) of wind turbines.
EU Regional School - Kirkland Seminar
Prof. Dr. Angus Kirkland - Advanced Methods in High Resolution Transmission Electron Microscopy: Instrumentation, Simulation and Exit Wavefunction Reconstruction
Department of Materials
University of Oxford, United Kingdom
I³MS - Mortensen Seminar
Prof. Dr. Mikael Mortensen - Automating the Spectral Galerkin Method - High Performance Computing in Python
Department of Mathematics, University of Oslo, Norway
The spectral Galerkin method employs globally supported spectral basis functions (e.g., Fourier, Chebyshev, Legendre) in the Galerkin approximation. Due to its accuracy, the method is often favored in the study of fundamental physical phenomena in Cartesian domains, like turbulence and transitional flows. Until now there have been few tools available for solving PDEs with this method, at least not if one is aiming at high performance supercomputers. With the shenfun Python module (https://github.com/spectralDNS/shenfun) an effort is made towards automating the implementation of the spectral Galerkin method for simple (yet large in scale) tensor product domains. The user interface to shenfun is intentionally made very similar to FEniCS (https://fenicsproject.org). PDEs are represented through weak variational forms and solved using efficient, order optimal direct solvers, that are made possible by exploiting the structure of the operators (e.g., tri-/penta-diagonality and upper Hessenberg), that arise from clever choices of modified Chebyshev or Legendre bases. MPI decomposition is achieved through the recently released mpi4py-fft module (https://bitbucket.org/mpi4py/mpi4py-fft), and all developed solver may, with no additional effort, be run on supercomputers using thousands of processors. The shenfun package has, for example, been used to create Navier Stokes solvers for triply periodic domains as well as channels. This talk will give a demonstration of current capabilities and highlight Python as the powerful language it is for high performance scientific computing.
I³MS - Boyaval Seminar
Dr. Sebastien Boyaval - Modelling Micro-Structured Flows : Recent Results, and Application to Viscoelastic Fluids
Laboratoire d'hydraulique Saint-Venant, Ecole des Ponts ParisTech, France
CANCELED-I³MS - Chinesta Seminar
Prof. Dr. Francisco Chinesta - Hybrid-Twins: When Data-Driven Mechanics Joins Advanced Model Order Reduction to Define Real-Time Dynamic Data-Driven Application Systems
Department of Computational Mechanics, École Centrale de Nantes, France
In the previous (third) industrial revolution digital twins (able to emulate a physical system from the accurate solution of the mathematical model expected describing it) were major protagonists, making accurate analyses and designs possible. Numerical simulation is nowadays present in most of scientific fields and engineering domains, making possible the virtual evaluation of systems responses and alleviating the number of experiences on the real system that the numerical model represents. However, usually, virtual models (digital twins) are static, that is, they are used in the analysis and/or design of complex systems, but they are not expected to accommodate or assimilate data so as to define dynamic data-driven application systems. The characteristic time of standard simulation strategies is not compatible with the real-time constraints compulsory for control purposes or augmented reality environments.
Moreover, in practice, significant deviations between the predicted and observed responses are noticed, limiting the use of digital twins in many applications requiring online adaptation. In that situation control-based approaches were and are usually retained, in which the system is condensed into a goal-oriented transfer-function for which, despite of its effectiveness, the amount of information manipulated remains quite limited to do not compromise the compulsory real-time feedback.
The origin of the just referred deviations between predictions and measurements is due to (i) inaccuracies in the employed models that sometimes continue to be crude approximations/descriptions of the real systems; (ii) to the fact that in many cases models evolve in time in an “a priori" almost unpredictable manner; and (iii) inaccuracies in the determination of the model parameters or in their time-evolution.
Thus, nowadays, it is generally accepted the urgent need of more reliable modeling approaches as well as the dynamic assimilation of collected data on running simulations, for defining efficient Dynamic Data-Driven Application Systems - DDDAS. DDDAS consist of three main ingredients: (i) a simulation core able to solve complex mathematical or data-driven models under real-time constraints; (ii) advanced strategies able to assimilate data; and (iii) a mechanism to adapt the model online to evolving environments (that could imply the model change and not only the change of the parameters that an “a priori" assumed model involves). Hybrid-Twin embraces these three functionalities into a new paradigm in simulation-based engineering, and more concretely a cyber-physical-system framework.