Dr. Emre Özkaya, SciComp

Title:
A Two-level approach for design optimization of acoustic liners

Abstract:

In this talk, we present a two-level approach for design optimization of acoustic liners panels, which are commonly used to damp engine noise in turbofan engines. The suggested method combines an adjoint-based gradient search algorithm with a global search method applied on a Gaussian process surrogate model. In this way, we effectively exploit the benefits of both approaches to achieve a good compromise between the computational effort and the degree of freedom used in optimization. In the optimization level, a global search is performed with few design parameters employing a Gaussian process surrogate model. In the second level, using the global optimal solution as the initial setting for the refined design vector, an adjoint based gradient search procedure is started. The unsteady discrete adjoint solver, which is the essential ingredient of the optimization framework, has been developed using Algorithmic Differentiation (AD) techniques. The feasibility of the two-level approach is demonstrated by finding the optimal liner parameters of a turbofan engine by-pass duct.

Prof. Matthias Möller, TU Delft, Department of Applied Mathematics

Title:
Solving Compressible Flow Problems by Isogeometric Analysis

Abstract:

Isogeometric Analysis is a relatively new approach for  the numerical solution of PDE-problems especially on complex geometries. It can be considered as a natural generalisation of the Finite Element Methods that aims at narrowing the gap between computational geometry modelling and numerical analysis. The key idea to achieve this goal is to adopt a common description of geometries and solution approximations by, e.g., B-splines or Non-Uniform Rational B-Splines (NURBS).

In this talk, we present our approach to develop an isogeometric compressible flow solver. It builds upon the generalisation of the algebraic flux correction paradigm to multi-patch Isogeometric Analysis as universal building block for the design of positivity-preserving high-order discretisation. Our implementation adopts Fletcher’s group formulation, which makes it possible to express the assembly of linear and bilinear forms in terms of sparse matrix-vector multiplications and element-wise vector operations with pre-computed coefficient vectors and matrices, respectively. This approach overcomes the high computational costs that are typically observed in quadrature-based assembly algorithms for high-order isogeometric methods.

We moreover discuss strategies for the efficient implementation of the proposed algorithm on heterogeneous multi-/many-core architectures making use of fast and smart expression templates for the typical building blocks like state vectors, fluxes and flux-Jacobians. This approach is combined with just-in-time compilation to generate hardware-optimised compute kernels thereby associating single patches of the discretisation with individual compute devices. We finally address the computational potential of this approach to be combined with algorithmic differentiation to develop adjoint-based optimisation tools.

Dr. Max Langbein, RHRK

Title:
Pattern-matching methods in flow fields

Abstract:

Pattern recognition in vector fields helps to understand and visualize complex three-dimensional vector fields which are used e.g. to describe wind in weather simulations, wind/water channel experiments for vehicles, ocean flows, or electromagnetic fields.

Reasonable efficient methods of Pattern recognition in vector fields should use invariants to transformations under which the physical laws are preserved, i.e. Galilei- resp. Lorenz-Transformations.

The most important ones can be expressed as invariants of higher-order tensors which are calculated from the field. The kernel for collecting the pattern tensors has to be invariant (in case of higher-order moment tensors) or the filter kernels applied to achieve a robust derivative (in case of higher order derivative tensors).

Invariance under coordinate transformations is then easily achieved using total contractions of (tensor-products of) the calculated derivative or moment-tensors. A framework has been created to get a set of independent invariants calculated by the method mentioned beforehand. It will be shown how the invariants including topological ones can be classified and expressed with this method.

The goal of the workshop is to give an overview of recent research activities at SciComp. In addition, two collaborators from RWTH Aachen University as well as Würzburg University and a tentative new collaborator from WIAS Berlin will give invited presentations.

Program

December 14th

13:00 – 13:30 AG SciComp: Review 2016 and Outlook 2017
(Prof. N. Gauger, U. Hahn)

13:30 – 14:00 Frequency based preconditioning and smoothing for shape optimization
(J. Kusch, RWTH Aachen University)

14:00 – 16:00 AG SciComp: Scientific Short Presentations (10 minutes each)
(Dr. E. Özkaya, J. Abdel Hay, M. Sagebaum, T. Albring, B. Zhou, S. Günther, L. Kusch, Dr. J. Schüle, T. Dick, O. Burghardt)

16:00 – 16:30 Coffee Break

16:30 – 17:00 Automatic Generation of Hadamard Shape Derivatives and Approximate Shape Hessians
(Dr. S. Schmidt, Würzburg University)

18:00 Workshop Dinner

December 15th

11:30 – 13:00 Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations
(Dr. A. Linke, WIAS Berlin)

Dr. Alexander Linke, Forschungsgruppe Numerische Mathematik und Wissenschaftliches Rechnen, Weierstrass Institute for Applied Analysis and Stochastics

Title:
Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations

Abstract:

For more than thirty years it was thought that the efficient construction of pressure-robust mixed methods for the incompressible Navier-Stokes equations, whose velocity error is pressure-independent, was practically impossible. However, a novel, quite universal construction approach shows that it is indeed  rather easy to construct pressure-robust mixed methods. The approach repairs a certain (L2-)orthogonality between gradient fields and discretely divergence-free test functions, and works for families of arbitrary-order mixed finite element methods, arbitrary-order discontinuous Galerkin methods, and finite volume methods. Novel benchmarks for the incompressible Navier-Stokes equations show that the approach promises significant speedups in computational practice, whenever the continuous pressure is complicated.

Philipp Otte, MathCCES, RWTH Aachen

Title:
Stabilization of Lattice-Boltzmann Methods by Entropic Moment Closures

Abstract:

Over the past 25 years, the Lattice-Boltzmann Method (LBM) has risen to be a competitive player in the field of Computational Fluid Dynamics (CFD). The LBM owes its success to its simple structure and straight forward parallelization on modern-day architectures. Still, stability — especially for very large Reynold’s numbers — is an issue rendering it a problematic choice for properly simulating acoustics. In this talk, we extend the applicability of the LBM to solving the inviscid Linear Euler Equations. This is achieved by applying and extending the idea of entropic moment closures to linear collisions in the Lattice-Boltzmann framework. In contrast to most approaches for entropic collision operators, the post-collision state can be explicitly stated as linear combination of the pre-collision state avoiding the unpredictable optimization process inherent to most entropic collision operators.

Nicolas Dietrich, TU Kaiserslautern

Title:
Parallel Time Integration: An Overview

Abstract:

Due to the massive growth of parallel computers it is worth to take a look on methods to tackle differential equations with methods which are parallel in time. This is challenging due to the causality which is naturally present in differential equations. I present methods covering different types of parallel methods, namely shooting type, domain decomposition, multigrid and direct solvers. The talk will strongly depend on the article “50 Years of Time Parallel Time Integration” by Martin J. Gander who did a great job in covering the evolution of the field.

Stefanie Günther, SciComp

Title:
Parallel-in-Time Optimization with Unsteady PDEs

Abstract:

A simultaneous optimization framework for unsteady PDEs using the parallel-in-time software library XBraid is presented. XBraid provides a non-intrusive approach for parallelization in the time domain by applying an iterative multigrid reduction in time algorithm to existing sequential time-stepping codes. We develop a non-intrusive adjoint solver for XBraid that enhances these primal iterations by an iteration for computing adjoint sensitivities parallel in time. The adjoint sensitivities are then used in a simultaneous optimization method, namely the One-shot method which solves the optimization problem in the full space. We validate the time-parallel simultaneous optimization approach by applying it to an inverse design problem with unsteady PDEs that mimics the behavior of separated flows past bluff bodies.

Dr. Markus Rütten, Institut für Aerodynamik und Strömungstechnik, DLR

Title:
Strategies for the Reduction of Turbulent Viscous Drag

Abstract:

In this talks new (and not so new) ideas and strategies, which may help to reduce turbulent viscous drag, will be discussed. Focal point is the turbulent wall bounded flow with its characteristic turbulent boundary layer and associated characteristic turbulent structures of different scales within. Special attention is paid to the problem of self-formation process of turbulent structures, the derivation of suitable control strategies, their realization and, finally, their evaluation in regard to drag reduction.
Addressing the fundamental properties of turbulence in boundary layers the talk starts with basic observations stemming from experiments and numerical simulation which elucidate the decay of flow structures and the transport of energy to smaller scales but also the formation of large scale turbulent structures and the associated process of turbulent self-regeneration cycle. Based on that an analytical approach is presented which has been used to derive one direction of technical concepts for turbulent drag reduction. Another direction of turbulent flow control technologies is associated with properties of the large scale turbulent flow structures in the log-layer region of the boundary layer. In this case control concepts have to face the problem of manipulating structures not close to the wall anymore. Hereto a new approach is presented and discussed.

Dr. Tatiana Kozubskaya, Computational Aeroacoustics Laboratory, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia

Title:
Higher-accuracy edge-based schemes on unstructured meshes for simulation of turbulent flows and acoustic fields

Abstract:

The talk begins with a review of edge-based schemes for unstructured meshes and history of their development. The recent modifications of these schemes aimed at their accuracy improvement can be divided into two main families. The first family exploits the idea of edge-based reconstruction of variables while the second one – the flux correction procedures. The talk presents our achievements in both directions. They are the SEBR (simplified edge-based reconstruction) and UFC (unsteady flux correction) schemes respectively. The numerical results are given for model and benchmark problems with smooth and discontinuous solutions.
The second part of the talk concerns the applied problems which we have computed or are still computing with the use of higher-accuracy edge-based schemes. In particular, they include simulations of transonic cavity flow, subsonic jets, aerodynamic and acoustic characteristics of helicopter rotor and some other problems. Most predictions of turbulent flows are carried out with the help of hybrid RANS-LES nonzonal approaches DES, DDES, IDDES implemented in our in-house code NOISEtte. The integral Ffowcs Williams Hawkings method is used for the calculation of acoustic farfields. A brief description of the code precedes the numerical results. The computations are performed on Russian supercomputers Lomonosov of MSU, MVS-10P of JSCC and KIAM cluster K100.