I³MS - Möller Seminar
Dr. Matthias Möller - Isogeometric Analysis for Compressible Flow Problems in Industrial Applications
Department of Applied Mathematics, Delft University of Technology, Netherlands
In this talk, we will present an isogeometric analysis (IgA) approach for the simulation of compressible flows that arise in industrial applications, in particular, in twin-screw rotary compressors.
In the first part of the talk, we present a positivity-preserving high-resolution scheme for compressible flows building upon the generalization of the algebraic flux correction paradigm  to isogeometric analysis. Our approach adopts Fletcher's group formulation  together with an efficient edge-based formation of system matrices and vectors from pre-computed coefficients to overcome the high computational costs that are typically observed in quadrature-based IgA-assembly algorithms.
Next to this algorithmic approach to achieving high computational efficiency, our implementation in the open-source library G+Smo (https://www.gs.jku.at/gismo) makes use of meta-programming techniques to combine the computational performance of several hardware-optimized linear algebra back-ends like Blaze, Eigen, and VexCL, with ease of implementation offered by the fluid dynamics expression-template library FDBB (https://mmoelle1.gitlab.io/FDBB). Just-in time compilation techniques are used to run the solver in heterogeneous computing environments.
In the second part of the talk, we describe an isogeometric approach for the creation of analysis-suitable multi-patch parameterizations for complex industrial applications and, in particular, for (parts of) twin-screw rotary compressors. Our approach builds on well-established elliptic grid generation techniques, which have been generalized to the IgA framework.
 C.A.J. Fletcher, The group finite element formulation, Computer Methods in Applied Mechanics and Engineering, 37, 225–244, 1983.
 D. Kuzmin, M. Möller, M. Gurris, Algebraic flux correction II. Compressible flow problems. In: Kuzmin et al. (editors) Flux-Corrected Transport: Principles, Algorithms, and Applications, 193–238. Springer, 2nd edition, 2012.