Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence

Multi-dimensional higher resolution methods for flow in porous media.

Currently standard first order single-point upstream weighting methods are employed in reservoir simulation for integrating the essentially hyperbolic system components. These methods introduce both coordinate-line numerical diffusion (even in 1-D) and cross-wind diffusion into the solution that is grid and geometry dependent. These effects are particularly important when steep fronts and shocks are present and for cases where flow is across grid coordinate lines. In this thesis, families of novel edge-based and cell-based truly multidimensional upwind formulations that upwind in the direction of the wave paths in order to minimise crosswind diffusion are presented for hyperbolic conservation laws on structured and unstructured triangular and quadrilateral grids in two dimensions. Higher resolution as well as higher order multidimensional formulations are also developed for general structured and unstructured grids. The schemes are coupled with existing consistent and efficient continuous CVD (MPFA) Darcy flux approximations. They are formulated using an IMPES (Implicit in Pressure Explicit in Saturation) strategy for solving the coupled elliptic (pressure) and hyperbolic (saturation) system of equations governing the multi-phase multi-component flow in porous media. The new methods are compared with single point upstream weighting for two-phase and three-component two-phase flow problems. The tests arc conducted on both structured and unstructured grids and involve full-tensor coefficient velocity fields in homogeneous and heterogeneous domains. The comparisons demonstrate the benefits of multidimensional and higher order multidimensional schemes in terms of improved front resolution together with significant reduction in cross-wind diffusion

Variational Fluid Motion Estimation with Physical Priors

In this thesis, techniques for Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) are developed that are based on variational methods. The basic idea is not to estimate displacement vectors locally and individually, but to estimate vector fields as a whole by minimizing a suitable functional defined over the entire image domain (which may be 2D or 3D and may also include the temporal dimension). Such functionals typically comprise two terms: a data-term measuring how well two images of a sequence match as a function of the vector field to be estimated, and a regularization term that brings prior knowledge into the energy functional. Our starting point are methods that were originally developed in the field of computer vision and that we modify for the purpose of PIV. These methods are based on the so-called optical flow: Optical flow denotes the estimated velocity vector inferred by a relative motion of camera and image scene and is based on the assumption of gray value conservation (i.e. the total derivative of the image gray value over time is zero). A regularization term (that demands e.g. smoothness of the velocity field, or of its divergence and rotation) renders the system mathematically well-posed. Experimental evaluation shows that this type of variational approach is able to outperform standard cross-correlation methods. In order to develop a variational method for PTV, we replace the continuous data term of variational approaches to PIV with a discrete non-differentiable particle matching term. This raises the problem of minimizing such data terms together with continuous regularization terms. We accomplish this with an advanced mathematical method, which guarantees convergence to a local minimum of such a non-convex variational approach to PTV. With this novel variational approach (there has been no previous work on modeling PTV methods with global variational approaches), we achieve results for image pairs and sequences in two and three dimensions that outperform the relaxation methods that are traditionally used for particle tracking. The key advantage of our variational particle image velocimetry methods, is the chance to include prior knowledge in a natural way. In the fluid environments that we are considering in this thesis, it is especially attractive to use priors that can be motivated from a physical point of view. Firstly, we present a method that only allows flow fields that satisfy the Stokes equation. The latter equation includes control variables that allow to control the optical flow so as to fit the apparent velocities of particles in a given image pair. Secondly, we present a variational approach to motion estimation of instationary fluid flows. This approach extends the prior method along two directions: (i) The full incompressible Navier-Stokes equation is employed in order to obtain a physically consistent regularization which does not suppress turbulent flow variations. (ii) Regularization along the time-axis is employed as well, but formulated in a receding horizon manner contrary to previous approaches to spatio-temporal regularization. Ground-truth evaluations for simulated turbulent flows demonstrate that the accuracy of both types of physically plausible regularization compares favorably with advanced cross-correlation approaches. Furthermore, the direct estimation of, e.g., pressure or vorticity becomes possible

HETEROGENEOUS MULTI-SENSOR FUSION FOR 2D AND 3D POSE ESTIMATION

Sensor fusion is a process in which data from different sensors is combined to acquire an output that cannot be obtained from individual sensors. This dissertation first considers a 2D image level real world problem from rail industry and proposes a novel solution using sensor fusion, then proceeds further to the more complicated 3D problem of multi sensor fusion for UAV pose estimation. One of the most important safety-related tasks in the rail industry is an early detection of defective rolling stock components. Railway wheels and wheel bearings are two components prone to damage due to their interactions with the brakes and railway track, which makes them a high priority when rail industry investigates improvements to current detection processes. The main contribution of this dissertation in this area is development of a computer vision method for automatically detecting the defective wheels that can potentially become a replacement for the current manual inspection procedure. The algorithm fuses images taken by wayside thermal and vision cameras and uses the outcome for the wheel defect detection. As a byproduct, the process will also include a method for detecting hot bearings from the same images. We evaluate our algorithm using simulated and real data images from UPRR in North America and it will be shown in this dissertation that using sensor fusion techniques the accuracy of the malfunction detection can be improved. After the 2D application, the more complicated 3D application is addressed. Precise, robust and consistent localization is an important subject in many areas of science such as vision-based control, path planning, and SLAM. Each of different sensors employed to estimate the pose have their strengths and weaknesses. Sensor fusion is a known approach that combines the data measured by different sensors to achieve a more accurate or complete pose estimation and to cope with sensor outages. In this dissertation, a new approach to 3D pose estimation for a UAV in an unknown GPS-denied environment is presented. The proposed algorithm fuses the data from an IMU, a camera, and a 2D LiDAR to achieve accurate localization. Among the employed sensors, LiDAR has not received proper attention in the past; mostly because a 2D LiDAR can only provide pose estimation in its scanning plane and thus it cannot obtain full pose estimation in a 3D environment. A novel method is introduced in this research that enables us to employ a 2D LiDAR to improve the full 3D pose estimation accuracy acquired from an IMU and a camera. To the best of our knowledge 2D LiDAR has never been employed for 3D localization without a prior map and it is shown in this dissertation that our method can significantly improve the precision of the localization algorithm. The proposed approach is evaluated and justified by simulation and real world experiments

Mass Transfer in Multiphase Systems and its Applications

This book covers a number of developing topics in mass transfer processes in multiphase systems for a variety of applications. The book effectively blends theoretical, numerical, modeling and experimental aspects of mass transfer in multiphase systems that are usually encountered in many research areas such as chemical, reactor, environmental and petroleum engineering. From biological and chemical reactors to paper and wood industry and all the way to thin film, the 31 chapters of this book serve as an important reference for any researcher or engineer working in the field of mass transfer and related topics

Vortex Wake and Exhaust Plume Interaction, Including Ground Effect

Computational modeling and studies of the near-field wake-vortex turbulent flows, far-field turbulent wake-vortex/exhaust-plume interaction for subsonic and High Speed Civil Transport (HSCT) airplane, and wake-vortex/exhaust-plume interaction with the ground are carried out. The three-dimensional, compressible Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The turbulence models of Baldwin and Lomax, one-equation model of Spalart and Allmaras and two-equation shear stress transport model of Menter are implemented with the RANS solver for turbulent-flow modeling. For the near-field study, computations are carried out on a fine grid for a rectangular wing with a NACA-0012 airfoil section and a rounded tip. The focus of study is the tip-vortex development, the near-wake-vortex roll-up, and validation of the results with the available experimental data. For the far-field study, the computations of wake-vortex interaction with the exhaust-plume of a single engine of a medium-size subsonic aircraft in a holding condition and two engines of a HSCT in a cruise condition are carried out using an overlapping zonal method for several miles downstream. The overlapping zonal method has been carefully developed and investigated for accurate and efficient calculations of the far-field wake-vortex flow. The results of the subsonic flow are compared with those of a Parabolized Navier-Stokes (PNS) solver known as the UNIWAKE code. Next, the problem of wake-vortex/ground interaction is investigated. For the simulation of this problem, typical velocity profiles of a tip vortex with and without the exhaust-plume temperature profiles are used for inflow boundary conditions and the computations are carried out using the overlapping zonal method for long distances downstream. The effects of the exhaust-plume temperature on the vortex descent, ground boundary-layer separation, vortex rebound and vortex decay are studied and validated with the available experimental data. A parametric study, which covers the effects of atmospheric conditions such as axial wind, crosswind, wind shear, turbulence and, Reynolds number on vortex motion and dynamics near the ground, is also carried out

Numerical Boundary Condition Procedures

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed