Heart disease is the main cause of death today, and studying causes and treatments are of great interest. Blood flow simulations using computational fluid dynamics shows promise in providing insight into this area. This study builds upon previous work by Larsson et al. and Kronborg et al. who have developed a program for simulating the blood flow through patient specific left ventricles. More specifically we aimed to improve the accuracy of their blood flow simulation by accounting for the protruding structure of the endocardial wall, previously disregarded in the model due to the limitations in spacial accuracy of echocardiography. These structures, consisting of trabeculae carneae and papillary muscles, have been shown to have a significant impact on the blood flow. In a recent study, Sacco et al. proposed a solution were a porous layer could mimic the effects on the blood flow from these structures in a rigid heart model. Our study aimed to apply this modification to the left ventricle of the dynamic model using the Navier-Stokes-Brinkman flow equation and a subdomain defining the porous region. This study has been working towards the end goal of fully implementing the porous layer into the heart simulation. The equations needed have been formulated and simulations have been run on flow in a more simple setting to verify the model. The simulations show promise in being able to recreate the results from Sacco et al. but further development is needed before the porous model can be tested in the dynamic left ventricle model, most notably defining the porous subdomain in the dynamic model. We conclude that the porous domain will affect the flow, possibly breaking up vortices and reducing the wall shear stress. Confirming this requires additional studies, but the implementation of a porous domain would likely result in a more accurate simulation.

A three-dimensional CFD program was used to predict the flow field that would enter a downstream fan or compressor rotor under the influence of an upstream thermal distortion. Two distortion generation techniques were implemented in the model; (1) a thermal source and (2) a heated flow injection method. Results from the investigation indicate that both total pressure and velocity boundary conditions at the compressor face are made non-uniform by the upstream thermal distortion, while static pressure remains nearly constant. Total pressure at the compressor face was found to vary on the order of 10%, while velocity varies from 50-65%. Therefore, in modeling such flows, neither of these latter two boundary conditions can be assumed constant under these conditions. The computational model results for the two distortion generation techniques were compared to one another and evaluations of the physical practicality of the thermal distortion generation methods are presented. Both thermal distortion methods create total temperature distortion magnitudes at the compressor face that may affect rotor blade vibration. Both analyses show that holding static pressure constant is an appropriate boundary condition for flow modeling at the compressor inlet. The analyses indicate that in addition to the introduction of a thermal distortion, there is a potential to generate distortion in total pressure, Mach number, and velocity. Depending on the method of thermally distorting the inlet flow, the flow entering the compressor face may be significantly non-uniform. The compressor face boundary condition results are compared to the assumptions of a previous analysis (Kenyon et al., 2004) in which a 25 R total temperature distortion was applied to a computational fluid dynamics (CFD) model of a fan geometry to obtain unsteady blade pressure loading. Results from the present CFD analyses predict similar total temperature distortion magnitudes corresponding to the total temperature variation used in the Kenyon analyses. However, the results indicate that the total pressure and circumferential velocity boundary conditions assumed uniform in the Kenyon analyses could vary by the order of 2% in total pressure and approximately 8% in velocity distortion. This supports the previously stated finding that assuming a uniform total pressure profile at the compressor inlet may be an appropriate approximation with the presence of a weak thermal distortion, while assuming a constant circumferential velocity boundary condition is likely not sufficiently accurate for any thermal distortion. In this work, the referenced Kenyon investigation and others related to the investigation of distortion-induced aeromechanical effects in this compressor rotor have assumed no aerodynamic coupling between the duct flow and the rotor. A full computational model incorporating the interaction between the duct flow and the fan rotor would serve to alleviate the need for assuming boundary conditions at the compressor inlet. / Master of Science

The method of dual steepest descent is used to solve ordinary differential equations with nonlinear boundary conditions. A general boundary condition is B(u) = 0 where where B is a continuous functional on the nth order Sobolev space Hn[0.1J. If F:HnCO,l] —• L2[0,1] represents a 2 differential equation, define *(u) = 1/2 IIF < u) li and £(u) = 1/2 l!B(u)ll2. Steepest descent is applied to the functional 2 £ a * + £. Two special cases are considered. If f:lR —• R is C^(2), a Type I boundary condition is defined by B(u) = f(u(0),u(1)). Given K: [0,1}xR—•and g: [0,1] —• R of bounded variation, a Type II boundary condition is B(u) = ƒ1/0K(x,u(x))dg(x).

The objective of this research is to simulate the response of an isolated substructure such that the response of the substructure in isolation would be the same as the substructure within the structure. Generally, the behaviour of an isolated subsystem (substructure) subjected to dynamic loading is different than the behaviour of the same substructure within a system (structure). This is primarily caused by the boundary conditions that are imposed on the substructure from the surrounding subsystem in the entire structure. A new systematic approach (methodology) is developed for performing impact analysis on the isolated substructure. The developed technique is fundamentally based on enforcing the mode shapes around the boundary of the substructure in the full structure to be similar to the mode shapes of the isolated substructure. This is achieved by providing a consistent adjustment to the loading conditions (impact velocity and mass) to account for the loss of restraint at the interface with the full structure. Another important aspect of this research is experimental validation of proposed method. This method allows the experimental testing of an isolated substructure since the testing is performed by impacting the isolated substructure with an appropriate mass and velocity. In the finite element analysis, the structure is analyzed, and then the isolated substructure simulation is performed using the developed technique. The results obtained from the numerical simulations, for both the substructure in situ and the substructure in isolation, are compared and found to be in good agreement. For instance, the effective plastic strains, kinetic and internal energies for the substructure within the structure and the substructure in isolation range from 7% to 12% discrepancies between two analyses. The numerical simulations of a full structure are verified by performing a series of experimental impact tests on the full structure. Finally, the experimental applicability of the technique is studied and its results are validated with FE simulation of substructure in isolation. This problem of experimentally testing an isolated substructure had previously not been addressed. The comparisons of FE simulation and experimental testing are made based on the deformed geometries, out-of-plane deflections and accelerometer readings. For example, the out-of-plane deformations from the FE analysis and the experimental test were determined to be within 7% to 9%. The experimental validation and numerical simulations indicates the technique is reliable, repeatable and can predict dynamic response of the substructures when tested in isolation. / Thesis / Doctor of Philosophy (PhD)

Differential equations arise frequently in modeling of physical systems, often resulting in linear eigenvalue problems. However, when dealing with large physical domains, solving such problems can be computationally expensive. This thesis examines an alternative approach to solving these problems, which involves utilizing absorbing boundary conditions and a Dirichlet-to-Neumann maps to transform the large sparse linear eigenvalue problem into a smaller nonlinear eigenvalue problem (NEP). The NEP is then solved using augmented Newton’s method. The specific equation investigated in this thesis is the two-dimensional Helmholtz equation, defined on the interval (x, y) ∈ [0, 10] × [0, 1], with the absorbing boundary condition introduced at x = 1. The results show a significant reduction in computational time when using this method compared to the original linear problem, making it a valuable tool for solving large linear eigenvalue problems. Another result is that the NEP does not affect the computational error compared to solving the linear problem, which further supports the NEP as an attractive alternative method.

In this dissertation, we study the existence and nonexistence of positive solutions to some classes of singular p-Laplacian boundary value problems with a parameter. In the first study, we discuss positive solutions for a class of sublinear Dirichlet p- Laplacian equations and systems with sign-changing coefficients on a bounded domain of Rn via Schauder Fixed Point Theorem and the method of sub- and supersolutions. Under certain conditions, we show the existence of positive solutions when the parameter is large and nonexistence when the parameter is small. In the second study, we discuss positive radial solutions for a class of superlinear p- Laplacian problems with nonlinear boundary conditions on an exterior domain via degree theory and fixed point approach. Under certain conditions, we show the existence of positive solutions when the paprameter is small and nonexistence when the paramter is large. Our results provide extensions of corresponding ones in the literature from the Laplacian to the p-Laplacian, and can be applied to the challenging infinite semipositone case

This study seeks to validate a recently introduced global preconditioning technique for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cellbased, finite volume formulation is used, with Roe flux difference splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel (LU/SGS) nested sub-iterations. This choice allows one to retain time accuracy, and eliminates approximate factorization errors, which become dominant at low speed flows. The linearized flux Jacobians are evaluated by numerical differentiation. Higher-order discretization is constructed by means of the MUSCL approach. Locally one-dimensional characteristic variable boundary conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergentdivergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M ≈ 10E − 4). Some preliminary tests of fully unsteady flows are also conducted.

No description available.

No description available.

Modern silencers for heavy vehicle applications are designed to cancel out the sound generated by the effects of combustion and propagation of exhaust gases through the engine after-treatment system. The complex geometry within the compact silencer give rise to self generated (or flow-) noise that contribute to the total sound power radiated at the exhaust outlet. To evaluate the magnitude and spectral frequency content of this self-generated noise, accurate non-reflective boundary conditions need to be applied along with a solver optimized for low dissipation and dispersion of acoustic waves. Parametric studies have been preformed to construct and evaluate the non-reflectiveness of stretched grids in combination with the buffer-zone technique for low- to mid- frequency noise. The Proudman noise source model have been used to identify the sources of sound within the computational domain and Detached Eddy Simulations have been used with full silencer geometries. Finally, the non-reflective performance of the stretched grid and buffer-zone technique have been evaluated using the acoustic beamforming method to spatially filter out and estimate the amount of reflections present in the final simulations. Detached Eddy Simulations can with success be used to resolve flow noise in exhaust gas geometries and allow reasonable comparisons. Steady models have been included in the comparisons but can only be used to estimate the amount of production of acoustic energy, not the radiated sound pressure levels related to the suppression of sound due to flow characteristics within the silencer geometries. Finally, the rough beamforming method confirmed the function of the non-reflective boundary conditions by finding major differences in magnitude for the sound being radiated towards the measurement point in different directions. / Ljuddämpare för lastbilar och bussar är konstruerade för att dämpa det ljud som genereras i förbränningsmotorn och i avgasreningssystemet. Moderna ljuddämpare består av komplexa geometrier som avgaserna flödar igenom och som släcker ut oönskat ljud. När avgaserna, bärandes ljud ifrån förbränningsmotorn flödar i hög hastighet genom den komplexa geometrin alstras ytterligare buller, så kallat själv-genererat ljud. För att ta fram frekensspektrat och ljudtrycksnivån ifrån detta bidragande ljud kan Detached Eddy Simulations utföras. Denna metod av strömningsmekaniska beräkningar kräver dock icke-reflektiva randvilkor. Randvilkor som uppfyller kraven har konstruerats genom parameterstudier tillsammans med en numerisk lösare som med låg dissipation och dispersion beräknar de akustiska pertubationerna i fjärfältet på ett fysikaliskt korrekt sätt. Vidare har även akustiska källmetoder används för att uppskatta närfältets storlek. Magnituden hos de kvarvarande reflektionerna har sedan uppskattas med hjälp av en förenklad Beamforming metod. Detached Eddy Simulations kan på ett framgångsfullt sätt användas för att ta fram det egengenererade ljudet ifrån ljuddämpargeometrier och möjliggör därigenom rimliga jämförelser mellan olika avgasgeometrier. De akusiska källmetoderna kan med säkerhet anvädas för att uppskatta den akustiska effekten som genereras i geometrierna men kan inte användas för att ta fram de dämpande effekterna som turbulenta strukturer eller hastighetsgradienter medför. Den förenklade Beamforming metoden har även bekräftat funtionen hos de icke-reflectiva randvilkoren genom att påvisa stora skillander i den ljudnivån som radierars ifrån olika riktingar mot den punkt som anvädas för att extrahera ljuddämparens ljudtrycksnivå.