Consortium Contributions

1. A. Cano: CD-Adapco, Paris:

Automatic process for CFD simulation with Starccm+, from CAD surface to post-processing

In order to return optimisation results as fast as possible, automatic process has to be used.
In this work an automatic process using a Java routine is run to calculate the cost function as the pressure drop and the flow homogeneity of a car catalyst. Also the catalyst contains a porous medium to simulate the pressure drop into small holes. First, the Java routine needs a CAD surface and some parameters to perform the volume meshing. Then the boundary conditions are setup automatically. After that the run starts and gives to the user residuals convergence and global convergence of the cost functions.

2. M.M. Gregersen, A. Evgrafov, M.P. Sørensen, Technical University of Denmark, Kongens Lyngby:

Topology optimisation of heat conduction problems

We are solving a pure heat conduction problem in a square domain Ω with a heat sink at one boundary section and thermally insulated walls at the remaining boundaries. By application of topology optimisation, two materials with significantly different thermal conductivities are distributed inside the domain, in order to minimize the weighted average temperature T . The domain is evenly heated across the square with a constant heat source Q, and the amount of highly conducting material is limited to occupy a fraction β of the total domain |Ω|. The design field variable γ varies continuously between 0 and 1, corresponding to low conductivity D_low and high conductivity D_high material, respectively. The interpolation of the thermal diffusivity follows D_th (γ) = D_low + (D_high − D_low)γ^p, where p is a penalization factor enforcing a pure 0 − 1 solution by convergence of the optimisation routine.

We implement the problem in OpenFOAM using a continuous adjoint formulation. Thus, the primary and adjoint equations are solved in OpenFOAM and linked to an IPOPT optimisation solver. The above example problem has previously been solved by Bendsøe and Sigmund [1] using a Matlab implemented finite element solver linked with the MMA optimisation routine. In a second calculation we have correspondingly used the commercial finite element program Comsol linked to a Matlab implementation of the MMA routine to solve the same problem. The topology optimised patterns produced by this Comsol implementation correspond well with the pattern published in [1]. However, comparing the output from our OpenFOAM-IPOPT implementation with the previous results, the patterns are qualitatively different.

In collaboration with FE-Design we have incorporated our OpenFOAM example problem in the Tosca-Fluid framework, through which the OpenFOAM solver is linked to the MMA optimisation routine. The optimisation runs successfully, but also in this case the structural output is qualitatively different from both the Comsol-Matlab and the OpenFOAM-IPOPT results

References:

1. M.P. Bendsøe and O. Sigmund, Topology Optimization-Theory, Methods and Applications, Springer (Berlin, 2003).

3. G. Pierrot, M. Megahed, ESI, Paris:

Introducing next generation of CFD adjoint solvers: towards a solver-independent solution

One of the major problematic in industry is to settle down an overall design methodology with respect to some manufacturing objectives. For example, designing "greener" vehicles has become a big challenge for automotive companies. This can be achieved, e.g., by reducing the drag coefficient of the vehicle in order to increase its fuel efficiency.

Of course, if we want to make a step in this direction, the ability of computing efficiently the sensitivity of any given objective function with respect to some design parameters appears to be a corner stone feature. This is what provides so-called adjoint solvers that allow for computing the sensitivity map at a cost which is independent of the number of design parameters.

So far however, classical adjoint solvers, like ESI PAM-FLOW adjoint solver, have either been linked with some primal CFD solver or obtained via automatic differentiation, which can be quite tedious process and still rely on a solver-by-solver approach. This typically prevents to use the adjoint solver corresponding to CFD code A together with CFD results coming from code B.

The purpose of our speech is to introduce ESI's next generation of adjoint solver, based on an approach that we call solver-independant, aimed to circumvent this limitation. This will allow to conduct adjoint calculations together with any primal CFD solver.

4. M. Böhm, T. Schützle, P. Häußler, FE-Design GmbH, Karlsruhe:

Optimisation for Fluid Flow

Today’s industrial processes for optimisation in fluid flow problems are still far away from a broad and effective application of sensitivity based optimisation approaches. Common strategies are parameter-based workflows with, for example evolutionary algorithms or similar methods. These approaches are computationally very expensive and therefore limited in their possible application. The necessary manual introduction of parameters is often no straight forward and can often be seen as an optimisation problem by itself.

Optimality criteria approaches like in the commercial tool TOSCA Fluid, for example, can deal with a very huge number of parameters and do not need a user-defined parametrisation. Nevertheless, these methods do not provide a broad spectrum of objective functions.

Example cases based on an optimality criteria approach for topology optimisation as well as morphing-based shape optimisation are outlined to illustrate the current state for shape and topology optimisation in many industrial contexts. Today’s possibilities with these approaches are discussed and compared with the industrial requirements. An outlook towards the properties and new possibilities of sensitivity-based shape and topology optimisation as developed in the FLOWHEAD project is presented.

5. M. Böhm, T. Schützle, P. Häußler, FE-Design GmbH, Karlsruhe:

An Optimisation Framework for CFD

The realization of an optimisation workflow in computational fluid dynamics is a complex task involving different functional modules or even applications. Defining appropriate interfaces between those parts is imperative for realizing reliable and maintainable software. Moreover software used in industrial production environments has to provide a basic stability that is especially important for distributed applications in large cluster environments.
Based on these considerations the architecture for an optimisation tool is derived that demonstrates the industrial application of sensitivity based optimisation in conjunction with the open source CFD solver OpenFOAM. Details are presented for a framework that allows the integration of specialized modules with the target of getting a working FLOWHEAD “industrial demonstrator”.

The coupling of an OpenFOAM solver that provides the sensitivity information with the framework is realized as a runtime interface that exchanges data between solver and optimisation framework within a single solver iteration loop. The framework is designed to support topology optimisation, parameter-free shape optimisation and morphing-based shape optimisation. For each optimisation type the workflow is outlined and analysed with respect to the framework requirements. Preconditions for extending the framework to support parallelised optimisation workflows based on domain decomposition are presented. Optimisation specific preprocessing and post-processing tasks are examined with the focus on their role within the overall application.
An outlook is given that presents future implementation changes of the framework and highlights the expected timeline.

6. D. Jones, F. Christakopoulos, J.-D. Müller, Queen Mary, University of London:

Discrete adjoint code development using Automatic Differentiation

Early developments of adjoint codes followed the 'continuous' route, where the adjoint equations are first derived, then discretised. This approach is typically quick to implement for simple sets of equations and results in efficient computational codes. However, this approach does not scale well to more complex sets of equations and typically exhibits a lack of robustness with reduced convergence rates.

As an alternative, we follow the discrete approach where the adjoint is obtained from differentiating and transposing the code statements in the flow solver, hence we first discretise, then differentiate. The principal advantage is that due to the exact transposition of the system matrix of the flow code, the discrete adjoint inherits all its stability properties, resulting in a robust code. Moreover, the differentiation can be automated using Automatic Differentiation (AD) software tools. The main issue now becomes to help the AD tool by directives and re-structuring of the flow code such that the resulting adjoint is efficient in CPU and memory use. While AD tools are available for many languages, they are most developed for Fortran. We will focus on use of F90 in our presentation.

We demonstrate application of AD to two CFD codes. We differentiate our in-house compressible code which has been fully re-written in Fortran90 to demonstrate the potential of AD in deriving codes for first and second derivatives. Here we focus in particular on which features of F90 should be used to simplify AD, and which F90 constructs should be avoided as they currently are not digested by AD. We then demonstrate how AD-derived adjoint flux routines can be used in the time-stepping loops of the CFD code, including its convergence acceleration algorithms, to obtain an efficient adjoint code.
We also will show the progress toward the differentiation of a commercial incompressible flow code. The application of AD to the typical pressure correction scheme, which uses linear solvers for the flow and pressure blocks inside a Picard iteration, will be discussed and results for a bench code will be shown. As a second step, we will be dealing with the code constructs of the commercial code which was written in F90, but contains code constructs which currently are not handled by AD.

7. G. Yu, J.-D. Müller, Queen Mary, University of London:

Adjoint-based optimisation using CAD sensitivities

Significant progress has been made with adjoint solvers applied in design loops. `One-shot' methods that converge flow, adjoint and design variables simultaneously have been shown to achieve converged designs in 5-10 times the cost of running a CFD solver on a fixed geometry. However, these implementations require very frequent gradient evaluations and hence rely on very inexpensive gradient computation based on reverse-differentiation of the design parametrisation. At convergence, we have the optimal design in form of a modified mesh, but not as desired in form of an updated CAD form.

CAD-based optimisation has been shown for some limited cases only. This is due to the fact that for the closed-source CAD software we need to apply expensive finite-differencing to obtain the necessary sensitivities to close the chain rule in the computation of the gradient of the cost function with respect to the design variables. Moreover, these applications rely on a user-defined parametrisation which can be complex to define and may give only a very restricted representation of the design space.

As an alternative we propose to base the parametrisation on the surface description through NURBS patches, which is the form in which the CAD surface is exchanged between the analysis and pre-/postprocessing tools in the virtual chain. The location of the control points of the NURBS patches are used as design variables, subject to constraints on geometric continuity or additional manufacturing and build space constraints. The patch definition can be generically interpreted by any geometry kernel, such as the open-source kernel OpenCASCADE, and is hence open to algorithmic differentiation to supply the inexpensive derivatives required for 'one-shot' methods. We demonstrate the efficiency of the approach using our own restricted implementation of the NURBS geometry in F90 differentiated with the AD tool tapenade.

8. M. Sidorkiewicz, RSA, Billancourt:

CAD-based optimisation methods with application to the automotive industry

In parallel to the current development of adjoint-based optimization methods in the scope of FLOWHEAD, the automobile industry is actively searching for reduction of greenhouse effect gas emissions through numerical simulation. The aim of the presentation is to draw up the work in progress in the field of the CAD-based shape optimization methods and to shown some recent results around the powertrain and the external aerodynamic optimization.

Nowadays, the entire automotive CFD Product Development Process is only relying on CAD models. All the models contain native manufacturing parameters. But these parameters are not often the geometric variables we want to optimize. Either they are architectural parameters, or they are a bad combination of optimization variables. Taking into account these amount of parameters, moreover, requires a lot of computer resources and to know how to manage the global optimization problem. Hence the two main drawbacks of the CAD-based optimization are : suitable computer resources and the availability of a goal-oriented parametrization of the initial shape.

FlowHead fulfills these requirements : the adjoint sensibilities trace the path to the one-shot optimization on paramete-free geometries. In parallel to the current development in the scope of FlowHead, Renault keeps going to improve the classical CAD-based optimization process. Either on a CAD model directly provided by the project, ie. the optimization result is also directly integrated in the final vehicle, or on a "home made" template, simplified for now, built on the optimization purpose. These specific models integrate all the necessary optimization variables, defined by the CFD engineer . The optimization result is not a geometry, but some new conception rules (pareto, interactions plot, statistical surrogates) reused later in the project to manually perform an optimization (radiator grill,car roof, car sides, ...)

The aim of the presentation is to draw up the 2 approaches and to illustrate them with examples from the powertrain field (internal aerodynamic) and the external field (side mirror and vehicle).

9. E. Stavropoulou, M. Hojjat, R. Wüchner, K.-U. Bletzinger, Technical University, Munich:

A mesh regularisation approach for surface grids

The quality of the solution in finite element and finite volume methods strongly depends on the domain discretisation. Hence, a good mesh is certainly desired as it is a prerequisite for meaningful results. However, many of the mesh generation techniques are not able to provide a discretization with good element shapes in the entire domain, especially in the case of complex geometries.

Moreover, even if the quality of the generated mesh is acceptable, in applications which deal with varying geometries or involve moving boundaries, during the evolution of the computation, the quality of elements could deteriorate and severely distorted elements might occur. In extreme cases, the elements become degenerate and further progress of analysis is restricted. For instance, in shape optimisation problems and large deformation fluid-structure interaction simulations, the retaining of the initial discretisation properties is not guaranteed.

In this work, a regularization scheme is developed, which is generally applicable to all the aforementioned cases and offers an automatic control of the quality of the mesh, being parallely efficient for large scale computations. This global regularization method smoothens the mesh towards a desired target mesh by only solving a linear system of equations with number of unknowns as much as the degrees of freedom preserving the boundary of the mesh.

The generality of the method with respect to the field of applications is discussed and examples from shape optimisation, large structural deformation simulations and mesh quality improvement are shown as well.

References:

1. K.-U. Bletzinger, R. Wü̈chner, F. Daoud, N. Camprubi, Computational methods for form finding and optimization of shells and membranes, Computer Methods in Applied Mechanics and Engineering 194, pp. 3438-3452 (2005)
2. K.-U. Bletzinger,R. Wü̈chner, Stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy, International Journal for Numerical Methods in Engineering 14(2), pp. 131-145 (2008)

10. G. Todorov, J. Ovtcharova, B. Romanov, K. Kamberov, Technical University, Sofia:

Interfaces for embedding CFD optimisation workflows into the product development process

The study previews and analyses the current state of the art of embedding CFD analysis data into the product development process. An approach for embedding CFD workflows connected to optimisation process is developed, based on the performed analyses. The main target is to enhance the conventional development workflow as to reduce iterations and time. Particular focus is set on the primary step of design models data extraction and transfer to the optimisation module, including numerical model preprocessing. Specifics of data transfer to OpenFOAM platform are examined in connection to the developed in the FLOWHEAD project fluid optimisation module. Complete research results in interface conception, based on the proposed combined approach.

11. C. Othmer¹, K. C. Giannakoglou², A.S. Zymaris², D.I. Papadimitriou² and E.M. Papoutsis-Kiachagias², ¹Volkswagen AG, Wolfsburg, Germany, ²National Technical University of Athens, Athens, Greece

Adjoint Methods for Automotive Optimisation: Achievements and Challenges

While adjoint methods are a well-established design optimisation technique in the aeronautical industry for years already, their incorporation into the automotive development process is still in its infancy, with first automotive applications of adjoint methods dating back to just 5 years ago [1]. However, especially since the implementation of a basic adjoint solver within the open source CFD code OpenFOAM® [2], the development of sensitivity-based optimisation techniques for automotive applications has seen quite some progress: both for topological optimisation approaches [3,4] as well as on the side of shape optimisation [4]. While topological optimisation has become fully productive for certain ducted flow applications, the current state of sensitivity-based shape optimisation methods hardly comes up to industrial robustness requirements. This is mainly due to the complexity of the geometries prevalent in automotive applications, which makes the robust computation of shape sensitivities and also their efficient exploitation very delicate. Our recent progress in these challenging aspects of shape optimisation will be reported in the lecture: the introduction of an adjoint turbulence model for increased accuracy of the shape sensitivities [5] and a shape update method based on mesh morphing. Results of the application of these methods to a generic bluff body and to a Volkswagen concept car will be presented. Current deficiencies of the existing processes and the challenges of a further industrialization of adjoint-based automotive optimisation will be pointed out.

References:

1. C. Othmer, Ph. Ravier, and G. Pierrot, Adjoint methods for automotive CFD optimization, PUCA 2005, Tokyo, 2005.
2. C. Othmer, A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows, Int. J. Num. Meth. Fluids, 58: 862-877, 2008.
3. C. Hinterberger, M. Olesen, “Automatic geometry optimisation of exhaust systems based on surface sensitivities computed by a continuous adjoint CFD method in OpenFOAM”, SAE 2010-01-1278.
   
4. Th. Grahs, C. Othmer, T.T. Robinson, C.G. Armstrong, From packaging space to CAD geometry: Optimal ducted flows with sequenced topological and shape optimisation, Open Source CFD International Conference, Barcelona, 2009.
5. A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, C. Othmer, Continuous adjoint approach to the Spalart-Allmaras turbulence model, Computers and Fluids, 38: 1528-1538, 2009.

OpenFOAM® is a registered trademark of OpenCFD Ltd

12. A. Jaworski¹, L.Laniewski¹, J.-D. Müller² and J. Rokicki¹, ¹Warsaw University of Technology, Warsaw and ²Queen Mary, University of London, London:

Grid adaptation using adjoint sensitivities

Grid adaptation is present in CFD already for a long time however still there is a need for robust and efficient algorithms. Latest works [1,2,3] present adaptation and error estimation for functional outputs, however their implementation is not trivial. This paper shows two relatively straight forward methods for goal oriented grid adaptation. First one is using error indicator based on adjoint and nonlinear source term in flux. Second approach is based on sensitivity of certain functional output (e.g. drag or lift) to the movement of each mesh node.

This needs calculation of edge length sensitivities which can be very efficient when using Automatic Differentiation tools which allow to compute adjoint sensitivities with moderate implementation effort. Obtained sensitivities are used to create an anisotropic metric which is an input to mesh generator. Both approaches are compared with interpolation based adaptation methods.

References:

1. David A. Venditti and David L. Darmofal, Grid Adaptation for Functional Outputs: Application to Two-Dimensional Inviscid Flows, J. Comput. Phys. 176, 40-69 (2002)
2. Niles A. Pierce, Michael B. Giles, Adjoint and defect error bounding and correction for functional estimates, J. Comput. Phys. 200, 769-794, (2004)
3. Ralf Hartman, Error Estimation and Adjoint-Based Adaptation in Aerodynamics, ECCOMAS CFD 2006.

13. L. Laniewski, J.Rokicki, Warsaw University of Technology, Warsaw:

Using Complex Gaussian Process Models for Robust Optimisation of Expensive Black-box Functions

Robust optimisation of expensive black-box functions is a common task in engineering. In such problems parameter variations are important optimisation factor. In our study we address problem of finding an robust optimum of functions that are expensive to calculate. We use Gaussian random fields (derived from Kriging) as statistical model of these functions to approximate the influence of parameter variation. We also consider a general geometry uncertainty and reduction of high dimensional design space.

We conduct our study on a simple case of optimisation the energy loss of internal flow in a pipe. We consider a base 3D geometry and use mesh deformation as means of parametrization. We assume the geometry uncertainty to be Gaussian and to be spatially correlated. We draft a method of construction of geometry parametrization that both reduce the cost of design space exploration and simplify uncertainty quantification.

We propose an asynchronous distributed optimisation algorithm based on our response function model. Similar approach to Efficient Global Optimisation algorithm by Jones et al is used, however Expected Improvement criterion for sampling is modified.

14. S. Munday, J.Papper, J.Gines, ICON Technology and Process Consulting Ltd, London:

Analysis of the Effects of Using a Differentiated Turbulence Model for Adjoint Optimisation on Industrial Applications based on OpenFOAM®¹

Adjoint design methods are a highly promising class of techniques for greatly improving industrial design processes. The theory is well established, but industrialisation of the process – i.e. robust execution on testcases of realistic complexity – is still a work in progress. We will demonstrate the current state of an industrial implementation of adjoint optimisation in the OpenFOAM environment, analysing in particular the effects of using a differentiated turbulence model over the traditional frozen turbulence assumption on the accuracy, convergence and stability of the process on realistic internal and external flow geometries.

References:

1. Islam, M., et al., Application of Detached–Eddy Simulation for Automotive Aerodynamics Development, in SAE Paper 2009-01-0333. 2009.
2. SST.2007-RTD-1, Grant agreement no. 218626, FLOWHEAD – Technical Annex 1, Version 3.0, 28 March 2008.
3. Petropoulou, S., C. Othmer, and M. Sidorkiewicz, FlowHead: Adjoint optimisation for industrial CFD workflow processes, in Open Source CFD International Conference 2009. 2009: Barcelona.
4. De Villiers, E. and S. Petropoulou, An Efficient Adjoint-Based Method Applied on Vehicle Aerodynamic Optimisation, in OpenFOAM International Conference 2007. 2007: London, UK.
5. A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, C. Othmer, Continuous adjoint approach to the Spalart-Allmaras turbulence model, Computers and Fluids, 38: 1528-1538, 2009.
6. Othmer, C., A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. International Journal of Numerical Methods in Fluids, 58: 861-877, 2008.
7. Petropoulou, S., Industrial Optimisation Solutions based on OpenFOAM® technology, in V. European Conference on Computational Fluid Dynamics, June 2010: Lisbon, Portugal.

¹ OPENFOAM® is a registered trade mark of OpenCFD® Limited.
The content is not approved or endorsed by OpenCFD Limited, the producer of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks