Browsing by Author "Bangerth, Wolfgang, committee member"
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Item Open Access A fourth-order finite volume algorithm with adaptive mesh refinement in space and time for multi-fluid plasma modeling(Colorado State University. Libraries, 2022) Polak, Scott E., author; Gao, Xinfeng, advisor; Guzik, Stephen, committee member; Tomasel, Fernando, committee member; Ghosh, Debojyoti, committee member; Bangerth, Wolfgang, committee memberImproving our fundamental understanding of plasma physics using numerical methods is pivotal to the advancement of science and the continual development of cutting-edge technologies such as nuclear fusion reactions for energy production or the manufacturing of microelectronic devices. An elaborate and accurate approach to modeling plasmas using computational fluid dynamics (CFD) is the multi-fluid method, where the full set of fluid mechanics equations are solved for each species in the plasma simultaneously with Maxwell's equations in a coupled fashion. Nevertheless, multi-fluid plasma modeling is inherently multiscale and multiphysics, presenting significant numerical and mathematical stiffness. This research aims to develop an efficient and accurate multi-fluid plasma model using higher-order, finite-volume, solution-adaptive numerical methods. The algorithm developed herein is verified to be fourth-order accurate for electromagnetic simulations as well as those involving fully-coupled, multi-fluid plasma physics. The solutions to common plasma test problems obtained by the algorithm are validated against exact solutions and results from literature. The algorithm is shown to be robust and stable in the presence of complex solution topology and discontinuities, such as shocks and steep gradients. The optimizations in spatial discretization provided by the fourth-order algorithm and adaptive mesh refinement are demonstrated to improve the solution time by a factor of 10 compared to lower-order methods on fixed-grid meshes. This research produces an advanced, multi-fluid plasma modeling framework which allows for studying complex, realistic plasmas involving collisions and practical geometries.Item Open Access A framework for simultaneous photon detector readout system simulations for the deep underground neutrino experiment(Colorado State University. Libraries, 2020) Christensen, Anne R., author; Buchanan, Norm, advisor; Ross, Kate, committee member; Bangerth, Wolfgang, committee memberThis thesis will discuss the changes to the coding framework for the Deep Underground Neutrino Experiment (DUNE). DUNE is simulated in a coding framework, called Liquid Argon Software (LArSoft). The framework simulates the particle event, the photons produced due to interactions and the electronics. The electronic simulation framework for DUNE has been changed to improve functionality and ease of use. The electronics simulation has been modularized so electronic readout models can be directly compared. The changes to the framework will be described and validated in this thesis.Item Open Access An analysis of domain decomposition methods using deal.II(Colorado State University. Libraries, 2021) Rigsby, Christina, author; Tavener, Simon, advisor; Bangerth, Wolfgang, committee member; Heyliger, Paul, committee member; Liu, Jiangguo, committee memberIterative solvers have attracted significant attention since the mid-20th century as the computational problems of interest have grown to a size beyond which direct methods are viable. Projection methods, and the two classical iterative schemes, Jacobi and Gauss-Seidel, provide a framework in which many other methods may be understood. Parallel methods or Jacobi-like methods are particularly attractive as Moore's Law and computer architectures transition towards multiple cores on a chip. We implement and explore two such methods, the multiplicative and restricted additive Schwarz algorithms for overlapping domain decomposition. We implement these in deal.II software, which is written in C++ and uses the finite element method. Finally, we point out areas for potential improvement in the implementation and present a possible extension of this work to an agent-based modeling prototype currently being developed by the Air Force Research Laboratory's Autonomy Capability Team (ACT3).Item Open Access Full waveform inversion for ultrasound computed tomography in the deterministic and Bayesian settings(Colorado State University. Libraries, 2022) Ziegler, Scott, author; Mueller, Jennifer, advisor; Cheney, Margaret, committee member; Bangerth, Wolfgang, committee member; Rezende, Marlis, committee memberUltrasound computed tomography (USCT) is a noninvasive imaging technique in which acoustic waves are sent through a region and measured after transmission and reflection in order to provide information concerning that region. There are many reconstruction techniques for USCT which rely on linearization of the total pressure field, but this simplifying assumption often causes a loss of resolution and poor results in highly reflective media. Full waveform inversion (FWI) is a method popularized by the geophysical community which makes use of entire time-dependent pressure measurements and repeated solutions of the nonlinear wave equation. Due to this lack of linearization, FWI is able to produce high-fidelity sound speed reconstructions, albeit at a steep computational cost. In this dissertation, we explore the use of the FWI techniques in both the deterministic and Bayesian settings. For the deterministic case, an algorithm for FWI is derived which makes use of the adjoint method for the computation of functional derivatives and the software package k-Wave for the solution of the nonlinear wave equation. This algorithm is tested on numerical breast and lung phantoms for a variety of regularization functionals and parameters, where it displays an excellent ability to reconstruct the size and shape of inhomogeneities. For the lung phantom, a novel application of a structural similarity index regularization term is used with an Electrical Impedance Tomography prior to speed convergence and improve organ boundary delineation. In the Bayesian setting, a Metropolis-adjusted Langevin FWI algorithm is proposed and tested on a simplified breast phantom, with an emphasis on reducing computational expense. Preliminary results from this test show promise for future research on FWI in the Bayesian framework.Item Open Access Geometry considerations for high-order finite-volume methods on structured grids with adaptive mesh refinement(Colorado State University. Libraries, 2022) Overton-Katz, Nathaniel D., author; Guzik, Stephen, advisor; Gao, Xinfeng, advisor; Weinberger, Chris, committee member; Bangerth, Wolfgang, committee memberComputational fluid dynamics (CFD) is an invaluable tool for engineering design. Meshing complex geometries with accuracy and efficiency is vital to a CFD simulation. In particular, using structured grids with adaptive mesh refinement (AMR) will be invaluable to engineering optimization where automation is critical. For high-order (fourth-order and above) finite volume methods (FVMs), discrete representation of complex geometries adds extra challenges. High-order methods are not trivially extended to complex geometries of engineering interest. To accommodate geometric complexity with structured AMR in the context of high-order FVMs, this work aims to develop three new methods. First, a robust method is developed for bounding high-order interpolations between grid levels when using AMR. High-order interpolation is prone to numerical oscillations which can result in unphysical solutions. To overcome this, localized interpolation bounds are enforced while maintaining solution conservation. This method provides great flexibility in how refinement may be used in engineering applications. Second, a mapped multi-block technique is developed, capable of representing moderately complex geometries with structured grids. This method works with high-order FVMs while still enabling AMR and retaining strict solution conservation. This method interfaces with well-established engineering work flows for grid generation and interpolates generalized curvilinear coordinate transformations for each block. Solutions between blocks are then communicated by a generalized interpolation strategy while maintaining a single-valued flux. Finally, an embedded-boundary technique is developed for high-order FVMs. This method is particularly attractive since it automates mesh generation of any complex geometry. However, the algorithms on the resulting meshes require extra attention to achieve both stable and accurate results near boundaries. This is achieved by performing solution reconstructions using a weighted form of high-order interpolation that accounts for boundary geometry. These methods are verified, validated, and tested by complex configurations such as reacting flows in a bluff-body combustor and Stokes flows with complicated geometries. Results demonstrate the new algorithms are effective for solving complex geometries at high-order accuracy with AMR. This study contributes to advance the geometric capability in CFD for efficient and effective engineering applications.Item Open Access Hodge and Gelfand theory in Clifford analysis and tomography(Colorado State University. Libraries, 2022) Roberts, Colin, author; Shonkwiler, Clayton, advisor; Adams, Henry, committee member; Bangerth, Wolfgang, committee member; Roberts, Jacob, committee memberThere is an interesting inverse boundary value problem for Riemannian manifolds called the Calderón problem which asks if it is possible to determine a manifold and metric from the Dirichlet-to-Neumann (DN) operator. Work on this problem has been dominated by complex analysis and Hodge theory and Clifford analysis is a natural synthesis of the two. Clifford analysis analyzes multivector fields, their even-graded (spinor) components, and the vector-valued Hodge–Dirac operator whose square is the Laplace–Beltrami operator. Elements in the kernel of the Hodge–Dirac operator are called monogenic and since multivectors are multi-graded, we are able to capture the harmonic fields of Hodge theory and copies of complex holomorphic functions inside the space of monogenic fields simultaneously. We show that the space of multivector fields has a Hodge–Morrey-like decomposition into monogenic fields and the image of the Hodge–Dirac operator. Using the multivector formulation of electromagnetism, we generalize the electric and magnetic DN operators and find that they extract the absolute and relative cohomologies. Furthermore, those operators are the scalar components of the spinor DN operator whose kernel consists of the boundary traces of monogenic fields. We define a higher dimensional version of the Gelfand spectrum called the spinor spectrum which may be used in a higher dimensional version of the boundary control method. For compact regions of Euclidean space, the spinor spectrum is homeomorphic to the region itself. Lastly, we show that the monogenic fields form a sheaf that is locally homeomorphic to the underlying manifold which is a prime candidate for solving the Calderón problem using analytic continuation.Item Open Access Modeling and parametric study of end-gas autoignition to allow the realization of ultra-low emissions, high-efficiency heavy-duty spark-ignited natural gas engines(Colorado State University. Libraries, 2022) Bestel, Diego Bernardi, author; Windom, Bret, advisor; Marchese, Anthony, committee member; Olsen, Daniel, committee member; Bangerth, Wolfgang, committee memberEngine knock and misfire are barriers to pathways leading to high-efficiency Spark-Ignited (SI) Natural Gas (NG) engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by the low emission limits and the wide range of chemical reactivity in pipeline-quality natural gas. Depending on the region and the source of the natural gas, its reactivity, described by its Methane Number (MN), which is analogous to the Octane Number for liquid SI fuels, can span from 65 to 95. In order to realize diesel-like efficiencies, SI NG engines must be designed to operate at high Brake Mean Effective Pressures (BMEP), near or beyond knock limits, over a wide range of fuel reactivity. This requires a deep understanding of the combustion-engine interactions pertaining to flame propagation and End-Gas Autoignition (EGAI), i.e., the autoignition of the unburned gas (end gas) ahead of the flame front. However, EGAI, if controlled, provides an opportunity to increase SI NG engine efficiency by increasing the combustion rate and the total fraction of burned fuel, mitigating the effects of the slow flame speeds characteristic of natural gas fuels, which generally reduce BMEP and increase unburned hydrocarbon emissions. For this reason, to realize diesel-like efficiencies and ultra-low emissions on SI NG engines, this work proposes the study of the main parameters influencing the modeling and prediction of NG EGAI to allow for its control. In this work, a novel EGAI detection and onset determination method was developed to reliably quantify EGAI for data analysis and engine control. The new method allowed the prediction of EGAI on SI NG engines without the need to use engine- and operating-condition-dependent thresholds and reduced the error in quantifying the fraction of the total energy released by the EGAI event by up to 40%pts. One- and three-dimensional engine models were then developed to study the engine/fuel interactions that lead to NG EGAI and its performance benefits. These models, although having decent agreement with experimental data, showed the need to account for NOx chemistry when predicting NG EGAI due to a consistently later prediction of the EGAI onset (∼1.65 crank-angle degrees) and thus, a new reduced chemical mechanism for real NG fuels was developed containing NOx chemistry. The new reduced mechanism improved the EGAI onset prediction agreement to within ±0.5 crank-angle degrees and decreased simulation time during combustion by nearly 50% when using the further reduced AREIS50NOx chemical mechanism. These models were then used to study the role of NG composition on EGAI, evaluate the engine/fuel interactions leading to NG EGAI, and perform engine optimization while leveraging EGAI to increase thermal efficiency. Piston design optimization combined with a Controlled EGAI (C-EGAI) combustion mode allowed a Heavy-Duty (HD) SI NG engine to operate at diesel-like efficiencies, i.e., Brake Thermal Efficiency (BTE) ≥44%. Experimental and modeling data analysis revealed that earlier and faster heat release increases combustion efficiency by an average of 1% pts, increases work transferred to the piston resulting in a decrease in exhaust losses by 50% depending on the engine operating condition while slightly increasing heat losses. Finally, the simulation results revealed an opportunity to further enhance the BTE (up to 50%) by enabling C-EGAI combustion at leaner conditions, λ=1.4-1.6.Item Open Access Numerical algorithms for two-fluid, weakly-compressible flows(Colorado State University. Libraries, 2024) Brodin, Erik, author; Guzik, Stephen, advisor; Colella, Phillip, advisor; Gao, Xinfeng, committee member; Troxell, Wade, committee member; Bangerth, Wolfgang, committee memberA multifluid numerical method is developed for flows of two fluids in a single domain at low Mach numbers. An all-speed formulation of the Navier-Stokes equations governs the dynamics of both fluids and the level-set method defines the interface between them and the domain of each fluid. The algorithm represents velocity and pressure as single valued throughout the whole domain, and fluid dependent variables, density and bulk modulus, only in the domain of their respective fluid. The all-speed equations are not subject to the divergence-free velocity constraint through use of a redundant velocity equation, and are evolved in time using an implicit-explicit additive Runge-Kutta method resulting in a time step constrained only by the bulk fluid velocity. Each fluid is evolved conservatively with respect to the moving interface between them. Due to errors in the evolution in the interface, perturbations in the volume of each fluid, and thereby the density, can develop. A thermodynamically consistent correction is made to the position of the interface to reduce these unphysical perturbations. The algorithm developed here includes three novel contributions: (i) the use of a multifluid all-speed algorithm with a level-set method for evolution of the solution in time, (ii) a multifluid algorithm using the level-set to capture the interface in the weakly compressible regime that is thermodynamically consistent, and (iii) an initialization method for sharp corners in the level-set. Numerical tests have demonstrated that the algorithm exhibits the expected low Mach number behavior, achieves second order-accuracy, and ensures fluid volumes are bounded and convergent.Item Open Access The unconventional eyewall replacement cycle of Hurricane Ophelia (2005)(Colorado State University. Libraries, 2018) Razin, Muhammad Naufal Bin, author; Bell, Michael M., advisor; Rasmussen, Kristen L., committee member; Bangerth, Wolfgang, committee memberOne of the mechanisms proposed for the spin-up of the tropical cyclone (TC) mean tangential circulation is the convergence of absolute angular momentum above the boundary layer. This mechanism is important for the outer primary circulation and results in the broadening of the TC wind field. We hypothesize that the mid-level inflow associated with the stratiform precipitation in TC rainbands may be instrumental in spinning up the broader circulation, and may be important in the development of secondary eyewalls. Hurricane Ophelia (2005) underwent an unconventional eyewall replacement cycle (ERC) as it was a Category 1 storm located over cold sea surface temperatures near 23°C. The ERC was observed using airborne radar observations during the Hurricane Rainband and Intensity Change Experiment (RAINEX). Data was collected from the single-parabolic X-band radar aboard the National Oceanic and Atmospheric Administration (NOAA) P-3 aircraft and from the dual-beam X-band Electra Doppler Radar (ELDORA) aboard the Naval Research Laboratory (NRL) P-3 aircraft. The two aircraft flew simultaneously along Ophelia's primary rainband during a research flight beginning around 1700 UTC on 11 September 2005, allowing for quad-Doppler wind retrievals along the rainband. Analyses were conducted using a spline-based three-dimensional variational wind synthesis technique. Results showed a broadened tangential wind field associated with the ERC was observed in the stratiform-dominant rainbands of Ophelia. The broadening of the tangential wind field was collocated with the strongest radial advection of angular momentum through the stratiform mid-level inflow and is consistent with the proposed mechanism for TC intensity change.Item Open Access Three-dimensional reconstruction and finite element modeling of anuran middle ear biomechanics(Colorado State University. Libraries, 2021) Fleming, Rachel C., author; Hoke, Kim, advisor; Mueller, Rachel, committee member; Bangerth, Wolfgang, committee memberThe ancestors of modern-day amphibians were the first vertebrates to evolve a middle ear for land-based hearing. Today's amphibians retain a simple and effective middle ear structure similar to those of their ancestors, and the fundamental mechanisms of these ears may reflect those that served as foundations of hearing in terrestrial vertebrates. Understanding amphibian hearing mechanisms can therefore offer insights into the evolution of the more sophisticated hearing we observe in land-dwelling vertebrates today. Although the anatomy of the amphibian middle ear has been thoroughly described, it is not known to what extent various anatomical properties, such as material properties or shape and size of ear structures, influence middle ear movement and sound transduction. To achieve this, I created 3D finite element models of the middle ears of Rhinella marina and Arthroleptis tanneri, two anuran species with different ear geometry. To create these models, I segmented middle ear parts from the scan, processed them into volumetric FE models, and set up finite element simulations. I subjected both models to harmonic response simulations at a range of frequencies and measured the sensitivity of the model to changes in various parameters to determine their effects on sound transmission. This study presents a hypothesis-generating tool for ear mechanics research and a better understanding of the biomechanics of how variation in the middle ear affects sound transmission. Additionally, this study may inform future work on the fundamental principles of hearing in terrestrial vertebrates.Item Open Access Time integration for complex fluid dynamics(Colorado State University. Libraries, 2021) Christopher, Joshua C., author; Gao, Xinfeng, advisor; Guzik, Stephen M., committee member; Marchese, Anthony J., committee member; Bangerth, Wolfgang, committee memberEfficient and accurate simulation of turbulent combusting flows in complex geometry remains a challenging and computationally expensive proposition. A significant source of computational expense is in the integration of the temporal domain, where small time steps are required for the accurate resolution of chemical reactions and long solution times are needed for many practical applications. To address the small step sizes, a fourth-order implicit-explicit additive Runge-Kutta (ARK4) method is developed to integrate the stiff chemical reactions implicitly while advancing the convective and diffusive physics explicitly in time. Applications involving complex geometry, stiff reaction mechanisms, and high-order spatial discretizations are challenged by stability issues in the numerical solution of the nonlinear problem that arises from the implicit treatment of the stiff term. Techniques for maintaining a physical thermodynamic state during the numerical solution of the nonlinear problem, such as placing constraints on the nonlinear solver and the use of a nonlinear optimizer to find valid thermodynamic states, are proposed and tested. Verification and validation are performed for the new adaptive ARK4 method using lean premixed flames burning hydrogen, showing preservation of 4th-order error convergence and recovery of literature results. ARK4 is then applied to solve lean, premixed C3H8-air combustion in a bluff-body combustor geometry. In the two-dimensional case, ARK4 provides a 70× speedup over the standard explicit four-stage Runge-Kutta method and, for the three-dimensional case, three-orders-of-magnitude-larger time step sizes are achieved. To further increase the computational scaling of the algorithms, parallel-in-time (PinT) techniques are explored. PinT has the dual benefit of providing parallelization to long temporal domains as well as taking advantage of hardware trends towards more concurrency in modern high-performance computing platforms. Specifically, the multigrid reduction-in-time (MGRIT) method is adapted and enhanced by adding adaptive mesh refinement (AMR) in time. This creates a space-time algorithm with efficient solution-adaptive grids. The new MGRIT+AMR algorithm is first verified and validated using problems dominated by diffusion or characterized by time periodicity, such as Couette flow and Stokes second problem. The adaptive space-time parallel algorithm demonstrates up to a 13.7× speedup over a time-sequential algorithm for the same solution accuracy. However, MGRIT has difficulties when applied to solve practical fluid flows, such as turbulence, governed by strong hyperbolic partial differential equations. To overcome this challenge, the multigrid operations are modified and applied in a novel way by exploiting the space-time localization of fine turbulence scales. With these new operators, the coarse-scale errors are advected out of the temporal domain while the fine-scale dynamics iterate to equilibrium. This leads to rapid convergence of the bulk flow, which is important for computing macroscopic properties useful for engineering purposes. The novel multigrid operations are applied to the compressible inviscid Taylor-Green vortex flow and the convergence of the low-frequency modes is achieved within a few iterations. Future work will be focused on a performance study for practical highly turbulent flows.Item Open Access Wave propagation: laser propagation and quantum transport(Colorado State University. Libraries, 2021) Bragdon, Sophia Potoczak, author; Pinaud, Olivier, advisor; Bangerth, Wolfgang, committee member; Cheney, Margaret, committee member; Gelfand, Martin, committee memberThis dissertation consists of two independent projects, where wave propagation is the common theme. The first project considers modeling the propagation of laser light through the atmosphere using an approximation procedure we call the variational scaling law (VSL). We begin by introducing the Helmholtz equation and the paraxial approximation to the Helmholtz equation, which is the starting point of the VSL. The approximation method is derived by pairing the variational formulation of the paraxial Helmholtz equation with a generalized Gaussian ansatz which depends on the laser beam parameters. The VSL is a system of stochastic ODEs that describe the evolution of the Gaussian beam parameters. We will conclude with a numerical comparison between the variational scaling law and the paraxial Helmholtz equation. Through exploring numerical examples for increasing strengths of atmospheric turbulence, we show the VSL provides, at least, an order-one approximation to the paraxial Helmholtz equation. The second project focuses on quantum transport by numerically studying the quantum Liouville equation (QLE) equipped with the BGK-collision operator. The collision operator is a relaxation-type operator which locally relaxes the solution towards a local quantum equilibrium. This equilibrium operator is nonlinear and is obtained by solving a moment problem under a local density constraint using the quantum entropy minimization principle introduced by Degond and Ringhofer in \cite{degondringhofer}. A Strang splitting scheme is defined for the QLE in which the collision and transport of particles is treated separately. It is proved that the numerical scheme is well-defined and convergent in-time. The splitting scheme for the QLE is applied in a numerical study of electron transport in different collision regimes by comparing the QLE with the ballistic Liouville equation and the quantum drift-diffusion model. The quantum drift-diffusion model is an example of a quantum diffusion model which is derived from the QLE through a diffusive limit. Finally, it is numerically verified that the QLE converges to the solution to the quantum drift-diffusion equation in the long-time limit.Item Open Access Weak Galerkin finite element methods for elasticity and coupled flow problems(Colorado State University. Libraries, 2020) Harper, Graham Bennett, author; Liu, Jiangguo, advisor; Bangerth, Wolfgang, committee member; Guzik, Stephen, committee member; Tavener, Simon, committee member; Zhou, Yongcheng, committee memberWe present novel stabilizer-free weak Galerkin finite element methods for linear elasticity and coupled Stokes-Darcy flow with a comprehensive treatment of theoretical results and the numerical methods for each. Weak Galerkin finite element methods take a discontinuous approximation space and bind degrees of freedom together through the discrete weak gradient, which involves solving a small symmetric positive-definite linear system on every element of the mesh. We introduce notation and analysis using a general framework that highlights properties that unify many existing weak Galerkin methods. This framework makes analysis for the methods much more straightforward. The method for linear elasticity on quadrilateral and hexahedral meshes uses piecewise constant vectors to approximate the displacement on each cell, and it uses the Raviart-Thomas space for the discrete weak gradient. We use the Schur complement to simplify the solution of the global linear system and increase computational efficiency further. We prove first-order convergence in the L2 norm, verify our analysis with numerical experiments, and compare to another weak Galerkin approach for this problem. The method for coupled Stokes-Darcy flow uses an extensible multinumerics approach on quadrilateral meshes. The Darcy flow discretization uses a weak Galerkin finite element method with piecewise constants approximating pressure and the Arbogast-Correa space for the weak gradient. The Stokes domain discretization uses the classical Bernardi-Raugel pair. We prove first-order convergence in the energy norm and verify our analysis with numerical experiments. All algorithms implemented in this dissertation are publicly available as part of James Liu's DarcyLite and Darcy+ packages and as part of the deal.II library.