Lionel Mathelin from LIMSI-CNRS will give a talk about Flow Control and Uncertainty Quantification.

Title:

An Occam’s razor paradigm for the control of complex systems

Abstract:

Efficient control of complex systems involves ingredients such as robustness, reduced order modeling, observation and command. In this talk, we will discuss some of these ingredients with the concern that one only has a limited information about the system at hand. A stochastic identification strategy, relying on sparsity exploiting techniques, will first be discussed. It allows modeling the uncertain parameters of the system and accurately quantifying the uncertainty associated with quantities of interest. An observer for fluid flows, dedicated to an experimental context, will next be presented. It relies on an offline/online strategy. An approximation basis of the field to be estimated is first learnt (offline step) using some knowledge on the flow (PIV, simulations, etc.) and information provided by a few, wall-mounted, sensors. Online, the estimation is achieved by sparse recovery from the sole sensors information. Finally, a controller is derived based on an optimal control approach. Exploiting the sparsity of the response surface of the control command allows, once again, performance and efficiency.

Tim Albring, SciComp

Title:
Semi-automatic Transition from Simulation to Optimization

Abstract:

PDE-constraint optimization often relies on the adjoint-based sensitivity evaluation, where one distinguishes between the discrete and the continuous methods. Both approaches have their advantages and disadvantages, but they are both difficult to apply to complex models and require involved development. However, based on the abstract structure of the primal fixed-point solver often applied for the numerical solution of PDEs, we will demonstrate in this talk that it is possible to construct a discrete adjoint solver which enables the computation of consistent gradients in a robust way. While the development and maintenance of the adjoint solver is automatically performed along with the development of the primal solver it also directly inherits its convergence properties. Since the implementation is heavily based on advanced techniques of Algorithmic Differentation (AD), we will give additionally some introductory notes on this method of evaluating gradients in a computer program. Furthermore, application to the open-source multi-physics framework SU² used for aerodynamic shape optimization will finish the talk.

Markus Widhalm from the Institute of Aerodynamics and Flow Technology at DLR Braunschweig will be our guest.

Title:
Evaluating Stability Derivatives with a Linearized Frequency Domain Solver

Abstract:

Efficient and accurate prediction of derivatives from aerodynamic forces and moments of aircrafts are crucial for their flight stability and control. This requires numerical methods that resolve aerodynamic forces and moments for the complete range of flow conditions encountered during an aircraft flight envelope. The talk starts with an overview and discussion of the flight mechanic principle. A linear, ordinary, differential equation emerges and is the basis for many well known problems. Subsequently, the forcing function and their treatment to obtain accurate stability derivatives from aerodynamic forces will be shown in more detail which leads to the linear frequency domain solver (LFD). The LFD is a small disturbance approach. After all, a complex valued linear system of equations has to be solved. If flow conditions reach transonic and detached conditions, this linear system usually gets stiff and preconditioning methods are necessary to solve the equations. We will focus on the derivation of the LFD’s equation and numerical methods to enhance robustness. An important concern is the accuracy in the linearisation procedure. Examples of misleading results are discussed which occur due to simplifications in the linearisation. Finally, an outlook presents alternative numerical approaches for determining stability data.

Anil Nemili, SciComp

Title:
Optimal Active Separation Control on High-Lift Configurations

Abstract:

During the landing and take-off phases of a modern commercial aircraft, high-lift devices are used to generate extra amount of lift to reduce the landing and take-off speeds and to shorten the runway length. However, at high flap deflection angles, the flow over the flap is prone to turbulent separation on the suction side. This results in a rapid fall in the lift while the drag increases enormously. In order to delay or suppress the separation and to enhance the lift, active flow control techniques can be employed. In these techniques, jets of fluid are injected or sucked through a narrow slot to add momentum to the boundary layer. The additional momentum due to actuation causes re-energisation of the flow, which delays the separation and thus aerodynamic stalling. Typically, the intensity of the actuation is controlled by varying the parameters of actuation like amplitude, frequency, phase shift and blowing angles. Effective separation control and thus enhancement in aerodynamic performance can be achieved by finding optimal set of actuation parameters. An efficient way of finding the optimal set of actuation parameters is by using the gradient based optimisation algorithms combined with discrete adjoint method. Towards this objective, a discrete adjoint method has been developed for incompressible URANS equations. The adjoint code is generated by applying the Algorithmic Differentiation (AD) tool Tapenade to a primal URANS code. The performance of the adjoint solver in accurate computation of unsteady sensitivities will be demonstrated. Numerical results will be presented for optimal active separation control on several geometries, ranging from simple airfoils to practical high-lift configurations.

We will host Stephan Schmidt from the Chair of Mathematics IX (Scientific Computing) at University of Würzburg.

Title:
Large Scale Shape Optimization – Inverse Problems, Nodal Mesh Deformation and Discrete Differential Geometry

Abstract:

Techniques and ingredients for large scale shape optimization are considered and exemplified by problems in computational acoustics as well as electromagnetic inverse design and computational fluid dynamics. In addition to the typical challenges within PDE-constrained optimization, such as successfully computing the adjoint solution, several auxiliary problems have to be overcome here, such as finding a robust deformation strategy of the computational grid, both with respect to the deformation of the volume mesh as well as with respect to a reparameterization of the nodes on the surface mesh. To this end, techniques from computer graphics, mesh smoothing and discrete differential geometry are considered as well as how to interface those aspects with automatic code generation utilizing the FEniCS framework.

Christoph Garth, Computational Topology Group

Title:
Scientific Visualization Research @ TU Kaiserslautern

Abstract:

The aim of scientific visualization is to provide graphical representations of complex physical phenomena in order to assist scientific investigation and to allow inferences that are not apparent in numerical form. It is therefore an integral component of many scientific workflows and fundamentally supports the scientific computing paradigm. In the first part of the talk, I aim to provide an overview of ongoing research in scientific visualization in my group, which is primarily aimed at developing methods for very large and complex datasets. In this context, parallel algorithms for visualization and topological techniques are primary research objectives. The second part of the talk will go into detail on recent research on the visualization of multi-variate datasets, where correlations and similarities among different variables are of interest. I will describe recent results on the application of Pareto sets, a concept typically used in multi-criteria optimization, to visualize the interactions of multiple variables in a two- or three-dimensional datasets. The talk will conclude with a brief discussion of current research challenges and an outlook on future work.

Daniela Fußeder, Felix-Klein-Center for Mathematics.

Title:
On Shape Optimization in the Context of Isogeometric Analysis

Abstract:

In shape optimization, the communication between the geometric description and the analysis suitable model of the domain plays an important role as updating the geometric design in one optimization step results in a new domain for the analysis, and vice versa. By means of Isogeometric Analysis (IGA) the same model can be used for design and analysis, in contrast to classical Finite Element Methods. So IGA skips conversion between meshes, which may lead to significant benefits. Since the advent of Isogeometric Analysis it has been shown that IGA is suitable for shape optimization in structural mechanics and electromagnetism. In this presentation, we discuss some fundamental issues related to shape optimization based on IGA and specifically the representation of shape gradients. We use Isogeometric Analysis to solve the state equation, and gradient-based methods for the optimization. This involves shape sensitivities that are defined in terms of the abstract framework of shape calculus and that are computed by means of the same basis functions as for the analysis, B-splines or NURBS. In this way, a quite general class of functions for representing optimal shapes and their boundaries becomes available. Moreover, it is possible to re-use the data from the analysis for the gradient computation, which leads to an efficient implementation.

Maarten Blommaert, Forschungszentrum Jülich/SciComp

Title:
A Practical and in Parts Adjoint Based Gradient Computation Methodology for Efficient Optimal Magnetic Divertor Design in Nuclear Fusion Reactors

Abstract:

The first fusion reactor ITER is currently under construction in Cadarache, France. Meanwhile, fusion power plant conceptual design activities are intensified in Europe, US and Asia. The transition of fusion research from a purely physical science towards computational engineering is regarded as urgent in all ITER partner states.

Design of the particle and power exhaust system, the so-called divertor configuration, is known to be a key issue to evolve from experimental fusion reactors to commercial power plants. This divertor is designed to modify the magnetic field configuration such that strong plasma flows develop towards particular high heat flux wall components of the burning chamber. However, the excessive heat loads to these components can easily exceed material limits. The divertor design process is assisted by computationally extremely demanding plasma edge codes, simulating the complex physics of the plasma edge. In order to reduce design costs, adjoint based optimal design methods have recently been introduced for divertor shape design.

In this presentation, the focus is on the application of a similar methodology that enables adjoint based optimal design of the fusion tokomak’s magnetic configuration. However, sensitivities of the plasma edge grid generation process complicate adjoint based sensitivity calculation. We describe how these difficulties can be overcome by using a combined finite differences/continuous adjoint gradient computation. Moreover, an extensive analytical derivation of the partial derivatives of the plasma edge equations with respect to the magnetic field geometry is entirely avoided by using the finite difference approach through the forward plasma edge solver as well. Optimal design results are shown for realistic test cases on existing experimental fusion reactors.

Matthias Sonntag, SciComp

Title:
Finite Volume Subcell Shock Capturing for high order Discontinuous Galerkin methods

Abstract:

Discontinuous Galerkin methods of high order accuracy have the problem that shock waves travelling through grid cells introduce instabilities. The high order polynomial in coarse grid cell generates spurious oscillations when such an inner element jump has to be resolved. There exist different methods to circumvent these problems. One possible shock capturing, which is inspired by the finite volume methodology, is the approach of refining the grid in shock regions, while reducing the degree of the polynomials, often called hp-adaption. In general the reduction of the polynomial degree decreases the oscillations, while the resolution has to be preserved by the h-refinement.

In this talk a shock capturing for high order Discontinuous Galerkin methods is presented, which treates shock regions by Finite Volume techniques on a implicit subgrid. Due to the subcell approach the interior resolution on the Discontinuous Galerkin grid cells is preserved and the number of degrees of freedom remains the same, which enables a straightforward and fast implementation.