Optimal control of shock wave attenuation in single - and two-phase flow with application to ignition overpressure in launch vehicles

NASA and private launch providers have a need to understand and control ignition overpressure blast waves that are generated by a solid grain rocket during ignition. Research in accurate computational fluid dynamics prediction of the launch environment is underway. A clearer picture is emerging from empirical data which more precisely categorizes all the dissipative mechanisms present in droplet-shock interactions. In this dissertation, water droplets and their effects due to vaporization are represented as a control action and two new optimal control problems are formulated concerning unsteady shock wave attenuation. A single-phase control problem is formulated by representing the effect of droplet vaporization as an energy sink on the right hand side of the unsteady Euler Equations in one dimension. Results for the optimal distribution of equivalent mass of water vaporized for a given level of attenuation are presented. A two-phase control problem consists of solving for the initial optimal water droplet distribution. Results are presented for constrained and unconstrained water volume fraction distributions over increasing levels of attenuation. New adjoint-based algorithms were constructed which leave the final time free and satisfy all first order necessary conditions as well as avoid taking a variation at the shock front.http://archive.org/details/optimalcontrolof1094510658Approved for public release; distribution is unlimited

Smooth and Robust Solutions for Dirichlet Boundary Control of Fluid-Solid Conjugate Heat Transfer Problems

This work offers new computational methods for the optimal control of the conjugate heat transfer (CHT) problem in thermal science. Conjugate heat transfer has many important industrial applications, such as heat exchange processes in power plants and cooling in electronic packaging industry, and has been a staple of computational methods in thermal science for many years. This work considers the Dirichlet boundary control of fluid-solid CHT problems. The CHT system falls into the category of multi-physics problems. Its domain typically consists of two parts, namely, a solid region subject to thermal heating or cooling and a conjugate fluid region responsible for thermal convection transport. These two different physical systems are strongly coupled through the thermal boundary condition at the fluid-solid interface. The objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the system and a prescribed temperature profile and the cost of the control. This objective is realized by minimizing a nonlinear objective function of the boundary control and the fluid temperature variables, subject to partial differential equations (PDE) constraints governed by the coupled heat diffusion equation in the solid region and mass, momentum and energy conservation equations in the fluid region. Although CHT has received extensive attention as a forward problem, the optimal Dirichlet velocity boundary control for the coupled CHT process to our knowledge is only very sparsely studied analytically or computationally in the literature [131]. Therefore, in Part I, we describe the formulation of the optimal control problem and introduce the building blocks for the finite element modeling of the CHT problem, namely, the diffusion equation for the solid temperature, the convection-diffusion equation for the fluid temperature, the incompressible viscous Navier-Stokes equations for the fluid velocity and pressure, and the model verification of CHT simulations. In Part II, we provide theoretical analysis to explain the nonsmoothness issue which has been observed in this study and in Dirichlet boundary control of Navier-Stokes flows by other scientists. Based on these findings, we use either explicit or implicit numerical smoothing to resolve the nonsmoothness issue. Moreover, we use the numerical continuation on regularization parameters to alleviate the difficulty of locating the global minimum in one shot for highly nonlinear optimization problems even when the initial guess is far from optimal. Two suites of numerical experiments have been provided to demonstrate the feasibility, effectiveness and robustness of the optimization scheme. In Part III, we demonstrate the strategy of achieving parallel scalable algorithms for CHT models in Simulations of Reactor Thermal Hydraulics. Our motivation originates from the observation that parallel processing is necessary for optimal control problems of very large scale, when the simulation of the underlying physics (or PDE constraints) involves millions or billions of degrees of freedom. To achieve the overall scalability of optimal control problems governed by PDE constraints, scalable components that resolve the PDE constraints and their adjoints are the key. In this Part, first we provide the strategy of designing parallel scalable solvers for each building blocks of the CHT modeling, namely, for the discrete diffusive operator, the discrete convection-diffusion operator, and the discrete Navier-Stokes operator. Second, we demonstrate a pair of effective, robust, parallel, and scalable solvers built with collaborators for simulations of reactor thermal hydraulics. Finally, in the the section of future work, we outline the roadmap of parallel and scalable solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer processes

Fast Radiative-Transfer-Equation-Based Image Reconstruction Algorithms for Non-Contact Diffuse Optical Tomography Systems

It is well known that the radiative transfer equation (RTE) is the most accurate deterministic light propagation model employed in diffuse optical tomography (DOT). RTE-based algorithms provide more accurate tomographic results than codes that rely on the diffusion equation (DE), which is an approximation to the RTE, in scattering dominant media. However, RTE based DOT (RTE-DOT) has limited utility in practice due to its high computational cost and lack of support for general non-contact imaging systems. In this dissertation, I developed fast reconstruction algorithms for RTE-based DOT (RTE-DOT), which consists of three independent components: an efficient linear solver for forward problems, an improved optimization solver for inverse problem, and the first light propagation model in free space that fully considers the angular dependency, which can provide a suitable measurement operator for RTE-DOT. This algorithm is validated and evaluated with numerical experiments and clinical data. According to these studies, the novel reconstruction algorithm is up to 30 times faster than traditional reconstruction techniques, while achieving comparable reconstruction accuracy

Efficient Reduction Techniques for the Simulation and Optimization of Parametrized Systems:Analysis and Applications

This thesis is concerned with the development, analysis and implementation of efficient reduced order models (ROMs) for the simulation and optimization of parametrized partial differential equations (PDEs). Indeed, since the high-fidelity approximation of many complex models easily leads to solve large-scale problems, the need to perform multiple simulations to explore different scenarios, as well as to achieve rapid responses, often requires unaffordable computational resources. Alleviating this extreme computational effort represents the main motivation for developing ROMs, i.e. low-dimensional approximations of the underlying high-fidelity problem. Among a wide range of model order reduction approaches, here we focus on the so-called projection-based methods, in particular Galerkin and Petrov-Galerkin reduced basis methods. In this context, the goal is to generate low cost and fast, but still sufficiently accurate ROMs which characterize the system response for the whole range of input parameters we are interested in. In particular, several challenges have to be faced to ensure reliability and computational efficiency. As regards the former, this thesis presents some heuristic approaches to approximate the stability factor of parameterized nonlinear PDEs, a key ingredient of any a posteriori error estimate. Concerning computational efficiency, we propose different strategies to combine the `Matrix Discrete Empirical Interpolation Method' (MDEIM) with a state approximation resulting either from a proper orthogonal decomposition or a greedy approach. Specifically, we exploit the MDEIM to develop fast and efficient ROMs for nonaffinely parametrized elliptic and parabolic PDEs, as well as for the time-dependent Navier-Stokes equations. The efficacy of the proposed methods is demonstrated on a variety of computationally-intensive applications, such as the shape optimization of an acoustic device, the simulation of blood flow in cerebral aneurysms and the simulation of solute dynamics in blood flow and arterial walls. %and coupled blood flow and mass transport in human arteries. Furthermore, the above-mentioned techniques have been exploited to develop a model order reduction framework for parametrized optimization problems constrained by either linear or nonlinear stationary PDEs. In particular, among this wide class of problems, here we focus on those featuring high-dimensional control variables. To cope with this high dimensionality and complexity, we propose an all-at-once optimize-then-reduce paradigm, where a simultaneous state and control reduction is performed. This methodology is applied first to a data reconstruction problem arising in hemodynamics, and then to several optimal flow control problems