Dr. Rubén Sánchez Fernández, SciComp

Title:
A Coupled Adjoint-Based Method for Aeroelastic Design in the Open-Source SU2 Suite

Abstract:

Computational Fluid-Structure Interaction (FSI) methods have reached a significant level of maturity, which has led to their incorporation into the analysis stage of industrial applications. However, optimising the structural and/or the aerodynamic performance in highly non-linear coupled FSI problems remains a challenging task, due to the high computational cost of evaluating the objective functions in this problem and their gradients. Adjoint methods have shown to be an efficient methodology for this latter task, as they can compute sensitivities with a computational cost independent of the number of design variables. On the other hand, their implementation is complex, particularly when the linearisation of the system equations is convoluted.
A novel technique for the evaluation of the coupled adjoint problem for FSI is presented. It is based on the consistent application of Algorithmic Differentiation to the fixed-point iterators of the subproblems. This approach makes the computation of the adjoint independent from the solution methods employed for the primal problem, and overcomes the usual limitation for most realistic applications, which is the need for an explicit construction of the analytic Jacobian of the coupled problem. The method poses no restrictions to the non-linearity of the physics in either the fluid or structural field, and it is amenable to partitioned solution methods for the primal and adjoint FSI problems.

Thomas Dick, SciComp

Title:
Stabilization of Discrete Adjoints by error attenuation

Abstract:

The Reverse Accumulation method for solving Discrete Adjoint problems often times requires the solution of a linear fixed point equation. If some of the components in this iteration are unstable, different stabilization techniques can be applied. In this talk we discuss how some of these implementations can be seen as a special kind of error attenuation.

Tobias Kattmann, BOSCH Renningen, Fluid Dynamics (CR/ARF3)

Title:
Unsteady Adjoints

Abstract:

Adjoint-based optimization of unsteady flows has not reached the maturity of its steady counterpart. A main reason is its larger demand of computational power and memory (to store the solution data). To approach the whole topic, a simple unsteady 1D-Diffusion solver together with an unsteady discrete-adjoint was implemented in python. A short outline of this code/results will be given. A possible method to reduce storage requirements for the primal solution data is to perform an (incremental) SVD over the temporal evolution of solution data and storing a low rank approximation. Again, this approach was implemented in python and simple test-cases were carried out to evaluate the method. Further, selected methods from literature for cost reduction of unsteady adjoints (a lot of which from the SU2-community, e.g. model order reduction via Harmonic Balance or temporal/spatial coarsening of the adjoint problem, …) are sketched and a classification is attempted, which is then open to the discussion. Comments, ideas and recommendations are highly appreciated.

Prof. Martin Geier, IRMB, TU Braunschweig

Title:
Aero-acoustical simulations with the lattice Boltzmann method

Abstract:

The lattice Boltzmann method for fluid mechanics has recently been improved concerning stability and accuracy by the application of a cumulant transform [1], by the use of quadric relaxation rates [2][3] and fourth order accurate advection [4]. At the same time, the method retains its geometrical flexibility, enabling us to simulate turbulent flow over and in fully resolved porous media [5]. Porous media is expected to play a key role in the reduction of airfoil noise in future commercial aircraft. The cumulant lattice Boltzmann method enables us to simulate the flow around the airfoil with porous edge and its acoustics together. In order to demonstrate the acoustic abilities of the lattice Boltzmann method we also present an auralization of an organ pipe simulation.

[1] Geier, Martin, et al. “The cumulant lattice Boltzmann equation in three dimensions: Theory and validation.” Computers & Mathematics with Applications 70.4 (2015): 507-547.
[2] Geier, Martin, Andrea Pasquali, and Martin Schönherr. “Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part I: Derivation and validation.” Journal of Computational Physics 348 (2017): 862-888.
[3] Geier, Martin, Andrea Pasquali, and Martin Schönherr. “Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion Part II: Application to flow around a sphere at drag crisis.” Journal of Computational Physics 348 (2017): 889-898.
[4] Geier, Martin, and Andrea Pasquali. “Fourth order Galilean invariance for the lattice Boltzmann method.” Computers & Fluids 166 (2018): 139-151.
[5] Kutscher, Konstantin, Martin Geier, and Manfred Krafczyk. “Multiscale simulation of turbulent flow interacting with porous media based on a massively parallel implementation of the cumulant lattice Boltzmann method.” Computers & Fluids (2018).

Prof. Siegfried Müller, IGPM, RWTH Aachen University
This is joint work with Dr. Giulia Deolmi and Prof. Wolfgang Dahmen.

Title:
Effective Boundary Conditions for Compressible Flows over Rough Boundaries

Abstract:

Simulations of a flow over a roughness are prohibitively expensive for small scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. In this talk the strategy originally developed by Achdou et al. [1] for incompressible flows is extended to compressible high-Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated and the results are compared with computations on a rough domain [2,3].

[1] Y. Achdou, O. Pironneau, F. Valentin, Eff ective boundary conditions for laminar flows over periodic rough boundaries, J. Comp. Phys., 147, 187–218, 1998.
[2] G. Deolmi, W. Dahmen, S. Müller, Effective boundary conditions for compressible flows over rough boundaries, Mathematical Models and Methods in Applied Sciences, 25(7), 1257-1297, 2015.
[3] G. Deolmi, W. Dahmen, S. Müller, Effective boundary conditions: a general strategy and application to compressible flows over rough boundaries, Communications in Computational Physics, 21(2), 358–400, 2017.

Dr. Emre Özkaya, SciComp

Title:
Primal-Dual Aggregation Method for Surrogate Modeling of Expensive Functions

Abstract:

Global design optimization using Partial Differential Equations requires very reliable surrogate modeling techniques since the underlying simulations may be computationally very expensive. In general, for such problems, the number of samples that can be generated to train the surrogate models is very limited due to restricted computational resources. On the other hand, recent developments in adjoint methods enable nowadays evaluation of gradient information at a reasonable computational cost for a wide variety of engineering problems. Therefore, a much richer data set can be acquired using an adjoint solver in a Design of Experiment. In the present work, we present a novel aggregation method, which enables the state of the art surrogate models to incorporate gradient information without causing robustness problems. Therefore, accurate surrogate models using few samples and large number of design parameters can be constructed. We also present results from several design optimization studies showing the efficiency and the robustness of the new method.

Dr. Stephan Schmidt, Uni Würzburg

Title:
Large Scale Geometric Inverse Problems and High Performance Computing

Abstract:

The primary concern of the presentation is geometric inverse problems governed by hyperbolic partial differential equations, meaning we are interested in reconstructing geometric objects such that they reproduce a measured echo of a scanning wave. There are a wide applications for problems of this type, including CFD, computational acoustics, Electrodynamics and mathematical imaging. We also study non-smooth problems that arise naturally when objects with kinks are to be reconstructed. To this end, we consider using Fenchel Duality and Raviart–Thomas spaces for Total Variation denoising of surfaces. The presentation concludes with numerical examples where FEM solvers are interfaced with 3D scanners to conduct denoising of real world objects and novel edge preserving mesh denoising techniques.

Matthias Freimuth, TU Kaiserslautern

Title:
Internal and External Coupling Approaches for Fluid-Structure Interaction Problems in SU2

Abstract:

In this talk two possibilities to handle Fluid-Structure Interaction(FSI) calculations under the usage of SU2 will be presented. For the first one, as given in [1], the coupling of the equations for fluid and structure is done within SU2. The coupled system is then solved by Block-Gauss-Seidel Iterations on its adjoint variables. The second approach is to couple the SU2 framework as solver for the fluid part of the problem with an external structure solver as discussed in [2].

[1]: Sanchez R, Albring T, Palacios R, Gauger NR, Economon TD, Alonso JJ. Coupled adjoint-based sensitivities in large-displacement fluid-structure interaction using algorithmic differentiation. Int J Numer Meth Engng. 2018;113:1081-1107. https://doi.org/10.1002/nme.5700.
[2]: Sanchez R, Kline HL, Thomas D, Variyar A, Righi M, Economon TD, Alonso JJ, Palacios R, Dimitriadis G, Terrapon V. Assessment of the fluid-structure interaction capabilities for aeronautical applications of the open-source solver SU2. ECCOMAS Congress 2016, Crete island, Greece, 5-10 June 2016.