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1 
Revealing the Physics of Multiphase Galactic Winds Through MassivelyParallel Hydrodynamics SimulationsSchneider, Evan Elizabeth, Schneider, Evan Elizabeth January 2017 (has links)
This thesis documents the hydrodynamics code Cholla and a numerical study of multiphase galactic winds. Cholla is a massivelyparallel, GPUbased code designed for astrophysical simulations that is freely available to the astrophysics community. A staticmesh Eulerian code, Cholla is ideally suited to carrying out massive simulations (> 2048 ³ cells) that require very high resolution. The code incorporates stateoftheart hydrodynamics algorithms including thirdorder spatial reconstruction, exact and linearized Riemann solvers, and unsplit integration algorithms that account for transverse fluxes on multidimensional grids. Operatorsplit radiative cooling and a dualenergy formalism for high mach number flows are also included. An extensive test suite demonstrates Cholla's superior ability to model shocks and discontinuities, while the GPUnative design makes the code extremely computationally efficient  speeds of 510 million cell updates per GPUsecond are typical on current hardware for 3D simulations with all of the aforementioned physics.
The latter half of this work comprises a comprehensive study of the mixing between a hot, supernovadriven wind and cooler clouds representative of those observed in multiphase galactic winds. Both adiabatic and radiativelycooling clouds are investigated. The analytic theory of cloudcrushing is applied to the problem, and adiabatic turbulent clouds are found to be mixed with the hot wind on similar timescales as the classic spherical case (45 t_cc) with an appropriate rescaling of the cloudcrushing time. Radiatively cooling clouds survive considerably longer, and the differences in evolution between turbulent and spherical clouds cannot be reconciled with a simple rescaling. The rapid incorporation of lowdensity material into the hot wind implies efficient massloading of hot phases of galactic winds. At the same time, the extreme compression of highdensity cloud material leads to longlived but slowmoving clumps that are unlikely to escape the galaxy.

2 
A Computational Model of the Ocular LensMalcolm, Duane Tearaitoa Kingwell January 2006 (has links)
The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the NernstPlank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electroosmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A onedimensional model of the Na+ , K+ , Cl and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the twodimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 1220% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300400% increase in Cl penetration and, unlike the first model, a Cl circulation between the poles and equator. This is significant since Cl is not an actively transported solute. These results highlight the strong structurefunction relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the twodimensional model was used to simulate agerelated changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The twodimensional model forms a foundation for future developments and applications.

3 
A Computational Model of the Ocular LensMalcolm, Duane Tearaitoa Kingwell January 2006 (has links)
The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the NernstPlank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electroosmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A onedimensional model of the Na+ , K+ , Cl and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the twodimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 1220% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300400% increase in Cl penetration and, unlike the first model, a Cl circulation between the poles and equator. This is significant since Cl is not an actively transported solute. These results highlight the strong structurefunction relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the twodimensional model was used to simulate agerelated changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The twodimensional model forms a foundation for future developments and applications.

4 
A Computational Model of the Ocular LensMalcolm, Duane Tearaitoa Kingwell January 2006 (has links)
The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the NernstPlank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electroosmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A onedimensional model of the Na+ , K+ , Cl and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the twodimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 1220% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300400% increase in Cl penetration and, unlike the first model, a Cl circulation between the poles and equator. This is significant since Cl is not an actively transported solute. These results highlight the strong structurefunction relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the twodimensional model was used to simulate agerelated changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The twodimensional model forms a foundation for future developments and applications.

5 
A Computational Model of the Ocular LensMalcolm, Duane Tearaitoa Kingwell January 2006 (has links)
The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the NernstPlank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electroosmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A onedimensional model of the Na+ , K+ , Cl and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the twodimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 1220% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300400% increase in Cl penetration and, unlike the first model, a Cl circulation between the poles and equator. This is significant since Cl is not an actively transported solute. These results highlight the strong structurefunction relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the twodimensional model was used to simulate agerelated changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The twodimensional model forms a foundation for future developments and applications.

6 
Finite difference and finite volume methods for wavebased modelling of room acousticsHamilton, Brian January 2016 (has links)
Wavebased models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional timestepping gridbased methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequencydependent wall impedances over nontrivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over nontrivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wavebased room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higherorder and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequencydomain analyses, as well as energy techniques whenever possible, allowing for stable and frequencydependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of nonCartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios.

7 
Blockbased Adaptive Mesh Refinement Finitevolume Scheme for Hybrid Multiblock MeshesZheng, Zheng Xiong 27 November 2012 (has links)
A blockbased adaptive mesh refinement (AMR) finitevolume scheme is developed for solution of hyperbolic conservation laws on twodimensional hybrid multiblock meshes. A Godunovtype upwind finitevolume spatialdiscretization scheme, with piecewise limited linear reconstruction and Riemannsolver based flux functions, is applied to the quadrilateral cells of a hybrid multiblock mesh and these computational cells are embedded in either bodyfitted structured or general unstructured grid partitions of the hybrid grid. A hierarchical quadtree data structure is used to allow local refinement of the individual subdomains based on heuristic physicsbased refinement criteria. An efficient and scalable parallel implementation of the proposed algorithm is achieved via domain decomposition. The performance of the proposed scheme is demonstrated through application to solution of the compressible Euler equations for a number of flow configurations and regimes in two space dimensions. The efficiency of the AMR procedure and accuracy, robustness, and scalability of the hybrid mesh scheme are assessed.

8 
Blockbased Adaptive Mesh Refinement Finitevolume Scheme for Hybrid Multiblock MeshesZheng, Zheng Xiong 27 November 2012 (has links)
A blockbased adaptive mesh refinement (AMR) finitevolume scheme is developed for solution of hyperbolic conservation laws on twodimensional hybrid multiblock meshes. A Godunovtype upwind finitevolume spatialdiscretization scheme, with piecewise limited linear reconstruction and Riemannsolver based flux functions, is applied to the quadrilateral cells of a hybrid multiblock mesh and these computational cells are embedded in either bodyfitted structured or general unstructured grid partitions of the hybrid grid. A hierarchical quadtree data structure is used to allow local refinement of the individual subdomains based on heuristic physicsbased refinement criteria. An efficient and scalable parallel implementation of the proposed algorithm is achieved via domain decomposition. The performance of the proposed scheme is demonstrated through application to solution of the compressible Euler equations for a number of flow configurations and regimes in two space dimensions. The efficiency of the AMR procedure and accuracy, robustness, and scalability of the hybrid mesh scheme are assessed.

9 
Simulations of Surfactant SpreadingWong, Jeffrey 01 May 2011 (has links)
Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical and experimental results.

10 
Magnetohydrodynamics simulation study of high density thermal plasmas in plasma acceleration devicesSitaraman, Hariswaran 17 October 2013 (has links)
The development of a Magnetohydrodynamics (MHD) numerical tool to study high density thermal plasmas in plasma acceleration devices is presented. The MHD governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in a plasma. A matrixfree implicit method is developed to solve these conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective flux Jacobian is derived for general unstructured grids. A Lower Upper Symmetric Gauss Seidel (LUSGS) technique is developed as part of the implicit scheme. A coloring based algorithm for parallelization of this technique is also presented and its computational efficiency is compared with a global matrix solve technique that uses the GMRES (Generalized Minimum Residual) algorithm available in the PETSc (Portable Extensible Toolkit for Scientific computation) libraries. The verification cases used for this study are the MHD shock tube problem in one, two and three dimensions, the oblique shock and the Hartmann flow problem. It is seen that the matrix free method is comparatively faster and shows excellent scaling on multiple cores compared to the global matrix solve technique. The numerical model was thus verified against the above mentioned standard test cases and two application problems were studied. These include the simulation of plasma deflagration phenomenon in a coaxial plasma accelerator and a novel high speed flow control device called the Rail Plasma Actuator (RailPAc). Experimental studies on coaxial plasma accelerators have revealed two different modes of operation based on the delay between gas loading and discharge ignition. Longer delays lead to the detonation or the snowplow mode while shorter delays lead to the relatively efficient stationary or deflagration mode. One of the theories that explain the two different modes is based on plasma resistivity. A numerical modeling study is presented here in the context of a coaxial plasma accelerator and the effect of plasma resistivity is dealt with in detail. The simulated results pertaining to axial distribution of radial currents are compared with experimental measurements which show good agreement with each other. The simulations show that magnetic field diffusion is dominant at lower conductivities which tend to form a stationary region of high current density close to the inlet end of the device. Higher conductivities led to the formation of propagating current sheet like features due to greater convection of magnetic field. This study also validates the theory behind the two modes of operation based on plasma resistivity. The RailPAc (Rail Plasma Actuator) is a novel flow control device that uses the magnetic Lorentz forces for fluid flow actuation at atmospheric pressures. Experimental studies reveal actuation ~ 10100 m/s can be achieved with this device which is much larger than conventional electrohydrodynamic (EHD) force based plasma actuators. A magnetohydrodynamics simulation study of this device is presented. The model is further developed to incorporate applied electric and magnetic fields seen in this device. The snowplow model which is typically used for studying pulsed plasma thrusters is used to predict the arc velocities which agrees well with experimental measurements. Two dimensional simulations were performed to study the effect of Lorentz forcing and heating effects on fluid flow actuation. Actuation on the order of 100 m/s is attained at the head of the current sheet due to the effect of Lorentz forcing alone. The inclusion of heating effects led to isotropic blast wave like actuation which is detrimental to the performance of RailPAc. This study also revealed the deficiencies of a single fluid model and a more accurate multifluid approach is proposed for future work. / text

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