Dr.-Ing. Mike Nicolai

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Computer simulations of fluid flow have steadily gained acceptance as an effective tool for evaluation of design modifications in the last decades. Shape optimization for fluids additionally offers a mathematical way to find optimal geometries. The design modifications can be expressed in a parameter vector. In our case the design modifications are realized by the T-spline representation of the sought shape. In this talk, we will introduce briefly the mathematical shape optimization problem using an idealized three-dimensional artificial graft as model example. The main focus will be on the approximation of the shape using T-Splines and the advantages compared with classical B-Spline variants like NURBS. For the model problem, we will report the results of a sensitivity-based optimization procedure applied to this problem as well as a mesh refinement study. At the end, we will show an overview of related shape optimization cases involving various geometries.

&#9656 Abstract

The difficulties arising in the numerical solution of PDE-constrained optimization problems are manifold. Key ingredients are the optimization strategy and the shape deformation method. Furthermore, the robustness of the optimal shape with respect to simulation parame- ters is of great interest. In this paper, we consider fluid flows described by the incompressible Navier-Stokes equations. Previous studies on artificial bypass grafts indicated the need for specific constitutive models to account for the non-Newtonian nature of blood; in particular, the constitutive model was shown to affect the solution of the shape optimization problem. We employ a shape optimization framework that couples a finite element solver with quasi-Newton- type optimizers and a Bezier spline shape parametrization. To compute derivatives of the optimal shapes with respect to viscosity, we transform the entire optimization framework by combining the automatic differentiation tools Adifor2 and TAPENADE. We demonstrate the impact of the geometry parametrization and of geometric constraints on the optimization outcome. Finally, we employ the transformed framework to compute the sensitivity of the optimal shape of by- pass grafts with respect to kinematic viscosity. The results show that the computed sensitivities predict very accurately the influence of viscosity changes on the optimal shape. The proposed methodology provides a powerful tool to further investigate the necessity of intricate constitutive models by taking derivatives with respect to model parameters.

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Simulation programs are widely established as aids for designing flow channels. However, the programs lack the option of allowing the flow-channel geometry to improve itself autonomously. This deficit is now to be made good by an automatic optimization tool in the XNS software.

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This paper gives a brief introduction about our current work in the field of shape optimization for fluids. After a short problem description, the methodology is demonstrated by means of a 2D example. This is followed by the concept of 3D geometry handling using T-spline and NURBS surfaces. Finally, a 3D example is given.

Note: Mike presented this work there as a finalist in the BGCE Student Prize competition.

&#9656 Abstract

Over the last decade, computer simulations of fluid flow have steadily gained acceptance as an effective tool for evaluation of design modifications. The flow features in complex geometries such as blood pumps, as well as the evolution of those features resulting from design changes, are hard to predict even by experienced design engineers. Linking a suitable mathematical framework with appropriate models in order to evaluate shape modifications will ultimately allow not only to analyze flow features but also to compute an optimal design directly. Such a framework requires an immense amount of computing power, which makes it a perfect candidate to exploit the potential of parallel processing on high-performance systems such as the J¨ulich Blue Gene/L.

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A parallel solver for incompressible fluid flow simulation, used in biomedical device design among other applications, is discussed. The major compute- and communication-intensive portions of the code are described. Using unsteady flow in a complex implantable axial blood pump as a model problem, scalability characteristics of the solver are briefly examined. The code that exhibited so far good scalability on typical PC clusters is shown to suffer from a specific bottleneck when thousands of processors of a Blue Gene are employed. After resolution of the problem, satisfactory scalability on up to four thousand processors is attained.

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The xns computational fluid dynamics code was successfully running on Blue Gene/L, however, its scalability was unsatisfactory until the first J ̈ulich Blue Gene/L Scaling Workshop provided an opportunity for the application developers and performance analysts to start working together. Investigation of solver performance pin-pointed a communication bottleneck that appeared with approximately 900 processes, and subsequent remediation allowed the application to continue scaling with a four-fold simulation performance improvement at 4,096 processes. This experience also validated the scalasca performance analysis toolset, when working with a complex application at large scale, and helped direct the development of more comprehensive analyses. Performance properties have now been incorporated to automatically quantify point-to-point synchronisation time and wait states in scan operations, both of which were significant for xns on Blue Gene/L.

&#9656 Abstract

Computational optimization is a growing, interdisciplinary area with many subfields such as protein folding, parameter identification and shape optimization for fluids to name just a few. The latter one is the combination of computational fluid dynamics (CFD) with optimization with main applications found in aerospace engineering and bioengineering. In bioengineering the optimization task is often made more difficult by the non-Newtonian, or micro-structured, nature of the flowing medium, such as blood. As motivation we will present a complex fluid flow in a ventricular assist device (VAD). The flow is modeled with the incompressible Navier-Stokes equations and solved using a stabilized space-time finite element method. To solve such problems we use a large in-house solver which runs on various parallel machines (Apple Xserve, Cray XD1, IBM Blue Gene, etc.) and is able to exploit the common communication interfaces for distributed memory systems (SHMEM, PVM and MPI). An optimization framework must fit seamlessly within this environments. With the assumption that the computational effort for optimization is very small compared with the CFD solutions we developed an in-house optimization framework. We will present such a framework which is capable of running on a single machine as well as on parallel machines. We will also show our strategy in handling the imbalance of the computational effort between optimization and CFD and show how a unified interface between them can interact with more then one optimization algorithm. As a step towards our goal of blood pump shape optimization, we will present a model problem from the bioengineering field including an objective function depending on blood damage as well as a parametrized geometric model of an idealized artificial graft.

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In this article we present an overview about our work on visualization of blood flow in ventricular assist devices (VADs). After presenting the project partners we introduce two specific VADs and their field of application. The numerical simulation of the blood flow in VADs is briefly described, along with the computational effort. We show in more depth the use of virtuel reality techniques and the benefits of this technology with respect to design of ventricular assist devices.

&#9656 Abstract

Shape optimization of engineering systems involving complex fluid flows has the potential to shorten the design cycle and to give the designer a way of evaluating various, sometimes non-intuitive, configuration changes. In bioengineering the optimization task is often made more difficult by the non-Newtonian, or micro-structured, nature of the flowing medium, such as blood.

As motivation, we present a direct problem involving complex fluid flow in a ventricular assistant device (VAD). The flow is modeled with the incompressible Navier-Stokes equations and solved using a stabilized space-time finite element method. The direct simulation seems relatively insensitive to refinements of the fluid constitutive model, incorporating shear-thinning or viscoelasticity. The simulation gives us important insights into causes of blood damage and suboptimal performance. Unfortunately this knowledge does not lead directly to better design, because of the complex problem behavior.

For a better design, we must go one step further and not just solve the direct problem but also perform a type of inverse analysis. In our case this would involve identification of shape parameters in a parametrized model of the blood pump which minimize objective function related, e.g., to blood damage.

On the way towards that goal, we will present a model problem including an objective function depending on blood damage as well as a parametrized geometric model of an idealized artificial graft. We will report the results of a sensitivity-based optimization procedure applied to this problem. The fluid may be considered in this problem as a Newtonian as well as a non-Newtonian one. Our results will highlight dependencies between velocity, shear-rate, constitutive model and optimal shape.