High Performance Computing Based Methods for Simulation and Optimisation of Flow Problems

The thesis is concerned with the study of methods in high-performance computing for simulation and optimisation of flow problems that occur in the framework of microflows. We consider the adequate use of techniques in parallel computing by means of finite element based solvers for partial differential equations and by means of sensitivity- and adjoint-based optimisation methods. The main focus is on three-dimensional, low Reynolds number flows described by the instationary Navier-Stokes equations

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions of a partial differential equation (PDE), representing a constraint for the minimization problem. The solution of these problems induce large computational costs due to the numerical discretization of PDEs and to iterative procedures usually required by numerical optimization (many-query context). In order to reduce the computational complexity, we take advantage of the reduced basis (RB) approximation for parametrized PDEs, once the state problem has been reformulated in parametrized form. This method enables a rapid and reliable approximation of parametrized PDEs by constructing low-dimensional, problem-specific approximation spaces. In case of PDEs defined over domains of variable shapes (e.g. in shape optimization problems) we need to introduce suitable, low-dimensional shape parametrization techniques in order to tackle the geometrical complexity. Free-Form Deformations and Radial-Basis Functions techniques have been analyzed and successfully applied with this aim. We analyze the reduced framework built by coupling these tools and apply it to the solution of optimal control and shape optimization problems. Robust optimization problems under uncertain conditions are also taken into consideration. Moreover, both deterministic and Bayesian frameworks are set in order to tackle inverse identification problems. As state equations, we consider steady viscous flow problems described by Stokes or Navier-Stokes equations, for which we provide a detailed analysis and construction of RB approximation and a posteriori error estimation. Several numerical test cases are also illustrated to show efficacy and reliability of RB approximations. We exploit this general reduced framework to solve some optimization and inverse problems arising in haemodynamics. More specifically, we focus on the optimal design of cardiovascular prostheses, such as bypass grafts, and on inverse identification of pathological conditions or flow/shape features in realistic parametrized geometries, such as carotid artery bifurcations

Aeronautical engineering: A special bibliography with indexes, supplement 41, February 1974

This special bibliography lists 514 reports, articles, and other documents introduced into the NASA scientific and technical information system in January 1974

A Spectral Discontinuous Galerkin method for incompressible flow with Applications to turbulence

In this thesis we develop a numerical solution method for the instationary incompressible Navier-Stokes equations. The approach is based on projection methods for discretization in time and a higher order discontinuous Galerkin discretization in space. We propose an upwind scheme for the convective term that chooses the direction of flux across cell interfaces by the mean value of the velocity and has favorable properties in the context of DG. We present new variants of solenoidal projection operators in the Helmholtz decomposition which are indeed discrete projection operators. The discretization is accomplished on quadrilateral or hexahedral meshes where sum-factorization in tensor product finite elements can be exploited. Sum-factorization significantly reduces algorithmic complexity during assembling. In this thesis we thereby build efficient scalable matrix-free solvers and preconditioners to tackle the arising subproblems in the discretization. Conservation properties of the numerical method are demonstrated for both problems with exact solution and turbulent flows. Finally, the presented DG solver enables long time stable direct numerical simulations of the Navier-Stokes equations. As an application we perform computations on a model of the atmospheric boundary layer and demonstrate the existence of surface renewal

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science