Higher-Order Unstructured Finite Volume Method for Computational Fluid Dynamics

ABSTRACT This dissertation presents a higher-order finite volume method (FVM) for computational fluid dynamics (CFD) for unstructured mesh topologies using Moving Least-Squares (MLS) as the backbone of the method. The MLS method is improved in several ways. First, the local stencil is weighed using a minimum volume enclosing ellipsoid (MVEE), which better encapsulates the local nodal topology than traditional spherical descriptions. Furthermore, a novel approach, known herein as Affine MLS, uses a spherical transformation of the ellipsoidal weights to map to the unit ball, where direct application of orthogonal polynomial bases can be used. This approach dramatically reduces the condition number of the MLS Moment/Gram matrix, especially on stretched grids which are commonly used for viscous flows and where traditional methods fail. All the MLS methods are also extended to use the Pivoting QR method for matrix inversion. The MLS method and improvements are extensively tested with several analytical functions for the full MLS reconstruction and fully diffuse derivatives. Optimal scaling parameters are also determined for the MLS method. Additionally, from work with MLS, the boundary conditions of the higher-order method are enforced with ghost nodes, an approach more commonly used in Immersed Boundary Methods. These boundary conditions do a better job of enforcing the boundary states, since they are included directly into the fluxes and gradients. Non-reflecting ghost nodes are implemented using the Navier–Stokes Characteristic Boundary Condition (NSCBC) for the inlet, outlet, and freestream boundary conditions for the first time in a finite volume ghost boundary node context. A higher-order viscous state reconstruction is presented as well wherein the MLS method is used to deter-mine the state and derivatives at the quadrature location. Some simple test cases are presented that highlight the benefits of the ghost node boundary conditions and viscous flux reconstruction. Finally, the higher-order CFD method is applied to the Taylor-Green Vortex (TGV) problem, a benchmark Large-Eddy Simulation (LES) case

Advances in Reduced-Order Modeling Based on Proper Orthogonal Decomposition for Single and Two-Phase Flows

This thesis presents advances in reduced-order modeling based on proper orthogonal decomposition (POD) for single and two-phase flows. Reduced-order models (ROMs) are generated for two-phase gas-solid flows. A multiphase numerical flow solver, MFIX, is used to generate a database of solution snapshots for proper orthogonal decomposition. Time-independent basis functions are extracted using POD from the data, and the governing equations of the MFIX are projected onto the basis functions to generate the multiphase POD-based ROMs. Reduced-order models are constructed to simulate multiphase two-dimensional non-isothermal flow and isothermal flow particle kinetics and three-dimensional isothermal flow. These reduced-order models are applied to three reference cases. The results of this investigation show that the two-dimensional reduced-order models are capable of producing qualitatively accurate results with less than 5 percent error with at least an order of magnitude reduction of computational costs. The three-dimensional ROM shows improvements in computational costs. This thesis also presents an algorithm based on mathematical morphology used to extract discontinuities present in quasi-steady and unsteady flows for POD basis augmentation. Both MFIX and a Reynolds Average Navier-Stokes (RANS) flow solver, UNS3D, are used to generate solution databases for feature extraction. The algorithm is applied to bubbling uidized beds, transonic airfoils, and turbomachinery seals. The results of this investigation show that all of the important features are extracted without loss in accuracy

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Higher-Order Unstructured Finite Volume Method for Computational Fluid Dynamics

ABSTRACT This dissertation presents a higher-order finite volume method (FVM) for computational fluid dynamics (CFD) for unstructured mesh topologies using Moving Least-Squares (MLS) as the backbone of the method. The MLS method is improved in several ways. First, the local stencil is weighed using a minimum volume enclosing ellipsoid (MVEE), which better encapsulates the local nodal topology than traditional spherical descriptions. Furthermore, a novel approach, known herein as Affine MLS, uses a spherical transformation of the ellipsoidal weights to map to the unit ball, where direct application of orthogonal polynomial bases can be used. This approach dramatically reduces the condition number of the MLS Moment/Gram matrix, especially on stretched grids which are commonly used for viscous flows and where traditional methods fail. All the MLS methods are also extended to use the Pivoting QR method for matrix inversion. The MLS method and improvements are extensively tested with several analytical functions for the full MLS reconstruction and fully diffuse derivatives. Optimal scaling parameters are also determined for the MLS method. Additionally, from work with MLS, the boundary conditions of the higher-order method are enforced with ghost nodes, an approach more commonly used in Immersed Boundary Methods. These boundary conditions do a better job of enforcing the boundary states, since they are included directly into the fluxes and gradients. Non-reflecting ghost nodes are implemented using the Navier–Stokes Characteristic Boundary Condition (NSCBC) for the inlet, outlet, and freestream boundary conditions for the first time in a finite volume ghost boundary node context. A higher-order viscous state reconstruction is presented as well wherein the MLS method is used to deter-mine the state and derivatives at the quadrature location. Some simple test cases are presented that highlight the benefits of the ghost node boundary conditions and viscous flux reconstruction. Finally, the higher-order CFD method is applied to the Taylor-Green Vortex (TGV) problem, a benchmark Large-Eddy Simulation (LES) case

Chapter 2 New Insights into the Roles of Dendritic Cells in Intestinal Immunity and Tolerance

Dendritic cells (DCs) play a critical key role in the initiation of immune responses to pathogens. Paradoxically, they also prevent potentially damaging immune responses being directed against the multitude of harmless antigens, to which the body is exposed daily. These roles are particularly important in the intestine, where only a single layer of epithelial cells provides a barrier against billions of commensal microorganisms, pathogens, and food antigens, over a huge surface area. In the intestine, therefore, DCs are required to perform their dual roles very efficiently to protect the body from the dual threats of invading pathogens and unwanted inflammatory reactions. In this review, we first describe the biology of DCs and their interactions with other cells types, paying particular attention to intestinal DCs. We, then, examine the ways in which this biology may become misdirected, resulting in inflammatory bowel disease. Finally, we discuss how DCs potentiate immune responses against viral, bacterial, parasitic infections, and their importance in the pathogenesis of prion diseases. We, therefore, provide an overview of the complex cellular interactions that affect intestinal DCs and control the balance between immunity and tolerance