Matching Items (24)
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- All Subjects: Mathematics
- Creators: Division of Teacher Preparation
- Status: Published
A level set approach for denoising and adaptively smoothing complex geometry stereolithography files
Description
Stereolithography files (STL) are widely used in diverse fields as a means of describing complex geometries through surface triangulations. The resulting stereolithography output is a result of either experimental measurements, or computer-aided design. Often times stereolithography outputs from experimental means are prone to noise, surface irregularities and holes in an otherwise closed surface.
A general method for denoising and adaptively smoothing these dirty stereolithography files is proposed. Unlike existing means, this approach aims to smoothen the dirty surface representation by utilizing the well established levelset method. The level of smoothing and denoising can be set depending on a per-requirement basis by means of input parameters. Once the surface representation is smoothened as desired, it can be extracted as a standard levelset scalar isosurface.
The approach presented in this thesis is also coupled to a fully unstructured Cartesian mesh generation library with built-in localized adaptive mesh refinement (AMR) capabilities, thereby ensuring lower computational cost while also providing sufficient resolution. Future work will focus on implementing tetrahedral cuts to the base hexahedral mesh structure in order to extract a fully unstructured hexahedra-dominant mesh describing the STL geometry, which can be used for fluid flow simulations.
A general method for denoising and adaptively smoothing these dirty stereolithography files is proposed. Unlike existing means, this approach aims to smoothen the dirty surface representation by utilizing the well established levelset method. The level of smoothing and denoising can be set depending on a per-requirement basis by means of input parameters. Once the surface representation is smoothened as desired, it can be extracted as a standard levelset scalar isosurface.
The approach presented in this thesis is also coupled to a fully unstructured Cartesian mesh generation library with built-in localized adaptive mesh refinement (AMR) capabilities, thereby ensuring lower computational cost while also providing sufficient resolution. Future work will focus on implementing tetrahedral cuts to the base hexahedral mesh structure in order to extract a fully unstructured hexahedra-dominant mesh describing the STL geometry, which can be used for fluid flow simulations.
ContributorsKannan, Karthik (Author) / Herrmann, Marcus (Thesis advisor) / Peet, Yulia (Committee member) / Frakes, David (Committee member) / Arizona State University (Publisher)
Created2014
Description
The dynamics of a fluid flow inside 2D square and 3D cubic cavities
under various configurations were simulated and analyzed using a
spectral code I developed.
This code was validated against known studies in the 3D lid-driven
cavity. It was then used to explore the various dynamical behaviors
close to the onset of instability of the steady-state flow, and explain
in the process the mechanism underlying an intermittent bursting
previously observed. A fairly complete bifurcation picture emerged,
using a combination of computational tools such as selective
frequency damping, edge-state tracking and subspace restriction.
The code was then used to investigate the flow in a 2D square cavity
under stable temperature stratification, an idealized version of a lake
with warmer water at the surface compared to the bottom. The governing
equations are the Navier-Stokes equations under the Boussinesq approximation.
Simulations were done over a wide range of parameters of the problem quantifying
the driving velocity at the top (e.g. wind) and the strength of the stratification.
Particular attention was paid to the mechanisms associated with the onset of
instability of the base steady state, and the complex nontrivial dynamics
occurring beyond onset, where the presence of multiple states leads to a
rich spectrum of states, including homoclinic and heteroclinic chaos.
A third configuration investigates the flow dynamics of a fluid in a rapidly
rotating cube subjected to small amplitude modulations. The responses were
quantified by the global helicity and energy measures, and various peak
responses associated to resonances with intrinsic eigenmodes of the cavity
and/or internal retracing beams were clearly identified for the first time.
A novel approach to compute the eigenmodes is also described, making accessible
a whole catalog of these with various properties and dynamics. When the small
amplitude modulation does not align with the rotation axis (precession) we show
that a new set of eigenmodes are primarily excited as the angular velocity
increases, while triadic resonances may occur once the nonlinear regime kicks in.
under various configurations were simulated and analyzed using a
spectral code I developed.
This code was validated against known studies in the 3D lid-driven
cavity. It was then used to explore the various dynamical behaviors
close to the onset of instability of the steady-state flow, and explain
in the process the mechanism underlying an intermittent bursting
previously observed. A fairly complete bifurcation picture emerged,
using a combination of computational tools such as selective
frequency damping, edge-state tracking and subspace restriction.
The code was then used to investigate the flow in a 2D square cavity
under stable temperature stratification, an idealized version of a lake
with warmer water at the surface compared to the bottom. The governing
equations are the Navier-Stokes equations under the Boussinesq approximation.
Simulations were done over a wide range of parameters of the problem quantifying
the driving velocity at the top (e.g. wind) and the strength of the stratification.
Particular attention was paid to the mechanisms associated with the onset of
instability of the base steady state, and the complex nontrivial dynamics
occurring beyond onset, where the presence of multiple states leads to a
rich spectrum of states, including homoclinic and heteroclinic chaos.
A third configuration investigates the flow dynamics of a fluid in a rapidly
rotating cube subjected to small amplitude modulations. The responses were
quantified by the global helicity and energy measures, and various peak
responses associated to resonances with intrinsic eigenmodes of the cavity
and/or internal retracing beams were clearly identified for the first time.
A novel approach to compute the eigenmodes is also described, making accessible
a whole catalog of these with various properties and dynamics. When the small
amplitude modulation does not align with the rotation axis (precession) we show
that a new set of eigenmodes are primarily excited as the angular velocity
increases, while triadic resonances may occur once the nonlinear regime kicks in.
ContributorsWu, Ke (Author) / Lopez, Juan (Thesis advisor) / Welfert, Bruno (Thesis advisor) / Tang, Wenbo (Committee member) / Platte, Rodrigo (Committee member) / Herrmann, Marcus (Committee member) / Arizona State University (Publisher)
Created2019
Description
Studies have shown that arts programs have a positive impact on students' abilities to achieve academic success, showcase creativity, and stay focused inside and outside of the classroom. However, as school funding drops, arts programs are often the first to be cut from school curricula. Rather than drop art completely, general education teachers have the opportunity to integrate arts instruction with other content areas in their classrooms. Traditional fraction lessons and Music-infused fraction lessons were administered to two classes of fourth-grade students. The two types of lessons were presented over two separate days in each classroom. Mathematics worksheets and attitudinal surveys were administered to each student in each classroom after each lesson to gauge their understanding of the mathematics content as well as their self-perceived understanding, enjoyment and learning related to the lessons. Students in both classes were found to achieve significantly higher mean scores on the traditional fraction lesson than the music-infused fraction lesson. Lower scores in the music-infused fraction lesson may have been due to the additional component of music for students unfamiliar with music principles. Students tended to express satisfaction for both lessons. In future studies, it would be recommended to spend additional lesson instruction time on the principles of music in order help students reach deeper understanding of the music-infused fraction lesson. Other recommendations include using colorful visuals and interactive activities to establish both fraction and music concepts.
ContributorsGerrish, Julie Kathryn (Author) / Zambo, Ronald (Thesis director) / Hutchins, Catherine (Committee member) / Division of Teacher Preparation (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points.
The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver.
Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data.
Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts.
The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6 and 25 degrees with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.
The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver.
Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data.
Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts.
The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6 and 25 degrees with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.
ContributorsMerrill, Brandon Earl (Author) / Peet, Yulia (Thesis advisor) / Herrmann, Marcus (Committee member) / Huang, Huei-Ping (Committee member) / Kostelich, Eric (Committee member) / Calhoun, Ronald (Committee member) / Arizona State University (Publisher)
Created2016
Description
There are two types of understanding when it comes to learning math: procedural understanding and conceptual understanding. I grew up with a rigorous learning curriculum and learned math through endless drills and practices. I was less motivated to understand the reason behind those procedures. I think both types of understanding are equally important in learning mathematics. Procedural fluency is the "ability to apply procedures accurately, efficiently, and flexibly... to build or modify procedures from other procedures" (National Council of Teachers of Mathematics, 2015). Procedural understanding may perceive as merely about the understanding of the arithmetic and memorizing the steps with no understanding but in reality, students need to decide which procedure to use for a given situation; here is where the conceptual understanding comes in handy. Students need the skills to integrate concepts and procedures to develop their own ways to solve a problem, they need to know how to do it and why they do it that way. The purpose of this 5-day unit is teaching with conceptual understanding through hands-on activities and the use of tools to learn geometry. Through these lesson plans, students should be able to develop the conceptual understanding of the angles created by parallel lines and transversal, interior and exterior angles of triangles and polygons, and the use of similar triangles, while developing the procedural understanding. These lesson plans are created to align with the eighth grade Common Core Standards. Students are learning angles through the use of protractor and patty paper, making a conjecture based on their data and experience, and real-life problem solving. The lesson plans used the direct instruction and the 5E inquiry template from the iTeachAZ program. The direct instruction lesson plan includes instructional input, guided practice and individual practice. The 5E inquiry lesson plan has five sections: engage, explore, explain, elaborate and evaluate.
ContributorsLeung, Miranda Wing-Mei (Author) / Kurz, Terri (Thesis director) / Walters, Molina (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
DescriptionAs an aspiring math teacher, I have created visual representation of my philosophy of education in the form of an embroidered skirt, bringing together my love of sewing and mathematics.
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
Description
As an aspiring math teacher, I have created visual representation of my philosophy of education in the form of an embroidered skirt, bringing together my love of sewing and mathematics.
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05