Dr. Josef Schüle, SciComp/RHRK

Title:
Using GPUs in SU2 code

Abstract:

GPUs may be used to reduce the required wall clock time in SU2 calculations. In this talk some early experiments on the usage of one GPU in implicit RANS calculations with SU2 are given. As the parallelism degree for the calculations is rather limited, one CPU thread will not be able to saturate several or even one GPU. Therefore this work focusses on sharing one or few GPUs by several threads, instead. Currently one step in the preconditioning of the linear equation solver has been analyzed there classical Gauss-Elimination of very small dense matrices has to be performed for all nodes repeatedly. Preliminary  results and ideas for further GPU usage will be given.

Dr. Emre Özkaya, SciComp

Title:
Robust Aerodynamic Shape Optimization Using Adjoint Assisted Surrogate Modeling

Abstract:

In the present work, we present an hybrid optimization framework for robust aerodynamic shape optimization. The suggested method combines a Kriging (also known as Gaussian process regression) based surrogate model with an adaptive sampling strategy assisted by the gradient information obtained from a discrete adjoint solver. In this way, it is possible to incorporate the uncertainties in design variables into the optimization algorithm. The feasibility of the suggested method is demonstrated by a comparative design optimization study using the benchmark test cases of the open source CFD software SU2.

Prof. Charles Swanson, NASA Langley Research Center and Old Dominion University, USA

Title:
Transport Equations: Mathematical and Discrete Issues

Abstract:

There is considerable effort to solve the problem of well-posedness, regularity, and global existence for the Navier-Stokes equations. While progress has been made for some particular cases, this Millennium problem remains unsolved in general. These issues also apply to the transport equation or equations for modeling the effects of turbulence. Without this mathematical foundation, one cannot know a priori if there exist a solution or possibly multiple solutions. Currently, scientists and engineers generally rely only upon numerical demonstrations to determine if there exist a realistic eddy viscosity from turbulence models, which primarily depends on solving transport equations. In this presentation, the mathematical and discrete issues concerning a representative two-equation turbulence model are examined. The challenges for convergence in steady state problems as well as unsteady problems, when considering a dual time-stepping algorithm, are discussed. Although the focus will be on a two-equation model, some representative convergence behaviors of a full Reynolds Stress Model (RSM) are also presented. Results are shown for three different airfoil cases at different flow conditions, which includes transonic flow conditions. Various issues in verification
of turbulence models are also briefly considered. A perspective on requirements for an effective and efficient numerical algorithm to solve the transport equations is also examined. In particular, the following issues are considered: (1) stiffness of the governing transport equations, (2) boundary conditions, (3) positivity and realizability, (3) boundary conditions, (4) strong solution algorithms, (5) linear and nonlinear stability, (6) analysis concerning behavior of the transport equations.

A pdf version of the slides can be found here.

Prof. Marc Pfetsch, Research Group Optimization, TU Darmstadt

Title:
Compressed Sensing and Discrete Optimization

Abstract:

The goal of this talk is to give an overview on compressed sensing from an discrete optimization/geometry point of view. The main problem in compressed sensing – the sparse representation problem – is to find the sparsest solutions of underdetermined linear equation systems. This problem is computationally hard, but can be efficiently solved by a linear program if certain conditions are satisfied. The talk will review some well known conditions and show that they are computationally hard to check. Moreover, the solution of this problem to global optimality will be discussed. The next step consists of presenting results on the unique recovery of integer solutions. Of course, even obtaining some feasible solution is hard in this case. Nevertheless, the potential of investing computational resources to obtain optimal solutions will be discussed.

Prof. Stefan Ulbrich, Nonlinear Optimization, TU Darmstadt

Title:
Robust Nonconvex PDE-Constrained Optimization based on Second Order Approximation Techniques and Reduced Order Models

Abstract:

We consider robust optimization techniques for nonconvex PDE-constrained problems involving uncertain parameters. The parameters are assumed to be contained in a given uncertainty set. This type of robust optimization problems are difficult to treat computationally and hence suitable approximations and solution methods are required. We propose and investigate an approximate robust formulation that employs a quadratic approximation (or only a linear approximation when appropriate) and can be solved efficiently by using a full-space formulation as mathematical program with equilibrium constraints (MPEC) or a reduced formulation. Moreover, we consider the application of reduced order models with a posteriori error estimation within the optimization method to reduce the number of required PDE-solves during the optimization.
We show applications to the robust geometry optimization of a permanent magnet synchronous motor and to the robust geometry optimization of load-carrying structures governed by the elastodynamic equations.

This is joint work with Oliver Lass and Philip Kolvenbach, TU Darmstadt.

Lisa Kusch, SciComp

Title:
Topology Optimization of Structures using the One-Shot Approach – Challenges and First Steps

Abstract:

The one-shot approach is traditionally used in the context of shape optimization with an underlying expensive partial differential equation constraint. If the solution process for the partial differential equation can be interpreted as a fixed point iteration, it can be augmented with an adjoint solver. Then, in the one-shot approach state and adjoint feasibility are pursued simultaneously with optimality using a suitable preconditioner.
We transfer the ideas of one-shot optimization to the field of topology optimization. The structural analysis involving geometrical and material non-linearities is realized with a Newton-like solver, that can be augmented by an adjoint solver. Several new challenges for one-shot topology optimization like projection methods and filter methods are discussed. Results are presented for topology optimization of nonlinear elastic structures in a two-dimensional setting to minimize compliance.

Ole Burghardt, SciComp

Title:
Conjugate heat transfer support within SU2

Abstract:

Computing estimations for heat fluxes from a heated solid’s wall into a cooling fluid flow is based on a good assumption of the wall’s temperature distribution. If such a distribution is not available, one in fact has to solve a coupled problem: The heating of the coolant fluid flow and the corresponding cooling of the solid itself, commonly called conjugate heat transfer or “CHT”.
In this talk, we will give an introduction to SU2’s recently developed multi-zone driver with CHT support and a simple test case so that one can quantify the errors that are made between a guessed (isothermal) temperature distribution and the physically more accurate one obtained by the coupling.

The specialty of our implementation then is its entire integration into the (heat and fluid flow) solver’s fixed point formulation that is used throughout in SU2. This way we can automatically solve the discrete adjoint problem of the coupled PDEs, resulting in physically accurate heat flux sensitivities for shape optimizations which we will address in the second half of the talk.

Tim Albring, SciComp

Title:
Constrained-based Shape Parameterization

Abstract:

The ability to drive a baseline shape to one with superior performance hinges on the quality of the shape parameterization. On the one hand it is often useful to delimit the design space, both to simplify the optimization problem and to avoid exploring regions known to be off-limits, often for non-aerodynamic reasons. On the other hand, pre-set deformation mechanisms can restrict the design space in irrelevant ways, needlessly hindering the discovery of valid designs. Deliberate, informed tailoring of the design space to individual problems is crucial for effective design.

In this talk we discuss a technique for creating custom, design-appropriate shape parameterizations of discrete surfaces. The idea is to leverage the smooth deformation properties of the Free-Form deformation, but to automate them and remove them from the designer’s direct control. Instead, the designer directly selects and manipulates any number of points on the surface and prescribes geometric constraints, while an automated system solves for a smooth deformation of the remainder of the surface that satisfies the constraints. Several applications in the field of internal and external flows will be presented, along with a comparison with traditional approaches. Furthermore the workflow in SU2 to set up an optimization using these features from the user’s perspective will be shown.