Current Search: Höflich, Peter, Ph. D. (x)
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 Title
 Diffuse Interface Method for TwoPhase Incompressible Flows.
 Creator

Han, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences,...
Show moreHan, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

In this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well...
Show moreIn this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well accepted phase field model. We propose a novel second order in time numerical scheme for solving the CHNS system. The scheme is based on a second order convexsplitting for the CahnHilliard equation and pressureprojection for the NavierStokes equation. We show that the scheme is massconservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of CahnHilliard equation and NavierStokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme. In addition, we propose a novel decoupled unconditionally stable numerical scheme for the simulation of twophase flow in a HeleShaw cell which is governed by the CahnHilliardHeleShaw system (CHHS). The temporal discretization of the CahnHilliard equation is based on a convexsplitting of the associated energy functional. Moreover, the capillary forcing term in the Darcy equation is separated from the pressure gradient at the time discrete level by using an operatorsplitting strategy. Thus the computation of the nonlinear CahnHilliard equation is completely decoupled from the update of pressure. Finally, a pressurestabilization technique is used in the update of pressure so that at each time step one only needs to solve a Poisson equation with constant coefficient. We show that the scheme is unconditionally stable. Numerical results are presented to demonstrate the accuracy and efficiency of our scheme. The CHNS system and CHHS system are two widely used phase field models for twophase flow in a single domain (either conduit or HeleShaw cell/porous media). There are applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, where multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. We present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models, the socalled CahnHilliardStokesDarcy system, together with the associated interface boundary conditions are derived by utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws and are consistent with thermodynamics. For the analysis of the CahnHilliardStokesDarcy system, we show that there exists at least a global in time finite energy solution by the compactness argument. A weakstrong uniqueness result is also established, which says that the strong solution, if exists, is unique in the class of weak solutions. Finally, we propose and analyze two unconditionally stable numerical algorithms of first order and second order respectively, for solving the CHSD system. A decoupled numerical procedure for practical implementation of the schemes are also presented. The decoupling is realized through explicit discretization of the velocity in the CahnHilliard equation and extrapolation in time of the interface boundary conditions. At each time step, one only needs to solve a CahnHilliard type equation in the whole domain, a Darcy equation in porous medium, and a Stokes equation in conduit in a separate and sequential fashion. Two numerical experiments, boundary driven and buoyancy driven flows, are performed to illustrate the effectiveness of our scheme. Both numerical simulations are of physical interest for transport processes of twophase flow in karst geometry.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9609
 Format
 Thesis
 Title
 Imprints of Explosion Conditions on LateTime Spectra of Type Ia Supernovae.
 Creator

Diamond, Tiara R., Höflich, Peter, Chicken, Eric, Collins, David C., Prosper, Harrison B., Riley, Mark A., Florida State University, College of Arts and Sciences, Department of...
Show moreDiamond, Tiara R., Höflich, Peter, Chicken, Eric, Collins, David C., Prosper, Harrison B., Riley, Mark A., Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

Type Ia supernovae (SNe Ia) play a vital role in the discrimination of different cosmological models. These events have been shown to be standardizable based on properties of their light curves during the earlytime photospheric phase. However, the distribution of types of progenitor system, the explosion trigger, and the physics of the explosion are still an active topic of discussion. The details of the progenitors and explosion may provide insight into the variation seen in Type Ia...
Show moreType Ia supernovae (SNe Ia) play a vital role in the discrimination of different cosmological models. These events have been shown to be standardizable based on properties of their light curves during the earlytime photospheric phase. However, the distribution of types of progenitor system, the explosion trigger, and the physics of the explosion are still an active topic of discussion. The details of the progenitors and explosion may provide insight into the variation seen in Type Ia supernova light curves and spectra, and therefore, allow for additional methods of standardization among the group. Latetime nearinfrared spectral observations for SNe Ia show numerous strong emission features of forbidden line transitions of cobalt and iron, tracing the central distribution of irongroup burning products. As the spectrum ages, the cobalt features fade as expected from the decay of 56Co to 56Fe. This work will show that the strong and isolated [Fe II] emission line at 1.644 μm provides a unique tool to analyze nearinfrared spectra of SNe Ia. Several new methods of analysis will be demonstrated to determine some of the initial conditions of the system. The initial central density, ρc, and the extent of mixing in the central regions of the explosion have signatures in the line profiles of latetime spectra. An embedded magnetic field, B, of the white dwarf can be determined using the evolution of the lines profiles. Currently magnetic field effects are not included in the hydrodynamics and radiation transport of simulations of SNe Ia. Normalization of spectra to the 1.644 μm line allows separation of features produced by stable versus unstable isotopes of iron group elements. Implications for potential progenitor systems, explosion mechanisms, and the origins and morphology of magnetic fields in SNe Ia, in addition to limitations of the method, are discussed. Observations of the latetime nearinfrared emission spectrum at multiple epochs allow for the first ever analysis of the evolution of the 1.644 μm line profile for a SNe Ia. These latetime data are really pushing the observational limits of current groundbased telescopes in terms of a dim target and low signaltonoise. The new analysis method presented in this work is used on observations of SN 2005df to constrain the initial conditions of those systems. Finally, the details and limitations of the method are presented for use with SN 2014J and future timeseries observations, which will dramatically increase in number and signaltonoise with the nextgeneration of telescopes and missions.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9322
 Format
 Thesis
 Title
 Exploration of the Interaction of Type Ia Supernovae with the Circumstellar Environment.
 Creator

Dragulin, Paul, Höflich, Peter, Yang, Wei, Huﬀenberger, Kevin, Roberts, Winston, Owens, Joseph F., Florida State University, College of Arts and Sciences, Department of Physics
 Abstract/Description

The identities of the progenitors of type Ia supernova (SN Ia) has long been under study and remains an unsolved problem of astrophysics. The answer to this question will impact cosmology and subfields such as galactic evolution. To help resolve this issue and determine what systems give rise to SN Ia, the relationships between progenitor systems, their winds, and their environments are here considered, and a theoretical tool is created to model the consequences. I present theoretical semi...
Show moreThe identities of the progenitors of type Ia supernova (SN Ia) has long been under study and remains an unsolved problem of astrophysics. The answer to this question will impact cosmology and subfields such as galactic evolution. To help resolve this issue and determine what systems give rise to SN Ia, the relationships between progenitor systems, their winds, and their environments are here considered, and a theoretical tool is created to model the consequences. I present theoretical semianalytic models for the interaction of stellar winds with the interstellar medium (ISM). To investigate a wide range of possible winds and environments, I developed and employ piecewise, semianalytical descriptions implemented in the code SPICE (Supernovae Progenitor Interaction Calculator for parameterized Environments, available on request), assuming spherical symmetry and powerlaw ambient density profiles. It is shown that a wide class of solutions can be found using the Buckingham Πtheorem. Semianalytic solutions allow us to test a wide variety of configurations, their dependencies on the wind and environment parameters, and find nonunique solutions within a set of observational constraints. SPICE may be used to model such interactions in different types of Supernovae (SNe), stellar winds, as well as modeling realistic feedback in star formation and large scale galactic evolution simulations. As one of the many potential applications for SPICE, here I study preconditioning of the environment of Type Ia Supernovae (SNe Ia), which may originate from two merging WDs, known as the double degenerate scenario (DD), or an accreting white dwarf star (WD) from a nondegenerate companion, known as the single degenerate scenario (SD). The wind of the progenitor systems may originate from the progenitor, a donor star, or an accretion disk (AD). The environment is determined by the ISM and/or the wind of the donor star or the wind of the progenitor star during a prior epoch. The free parameters are: the a) mass loss [m with dot above] , b) wind velocity v[subscript w], c) density distributions ∝ r[superscript s] of the ISM, and d)} the duration of the wind prior to the supernova explosion. I discuss the observational signatures with respect to light curves and high resolution spectra as tools to probe the environment of SNe Ia. The specific properties and evolution of the progenitor systems are found to leave unique imprints. During the progenitor evolution and with typical parameters in the SD scenario, the winds create a low density bubble surrounding the progenitor system and a highdensity shell. It is also found that accretion disk winds dominate the environment formation. Within a distance of several lightyears (ly), the densities are smaller by factors of 10²…⁴ compared to the environment. This explains the general lack of observed interaction in late time Supernova (SN) light curves for, at least, several years. The overdensities of the shells are between a factor of 4 to several hundred in case of constant density ISM and environments produced by stellar winds, respectively. The expansion velocity and width of the shell are typically 110% of both v[subscript w] and the contact discontinuity R[subscript C] and may produce narrow spectral lines as observed in some SNe Ia. Typically, narrow circumstellar lines of equivalent width ≈ 100 mÅ are found for uniform ISM typical in Spiral galaxies and ≈ 1 mÅ for wind environments. The outer layers of a SNe Ia expands with velocities of 10 to 30% of the speed of light and we may expect some interaction with the shells several years after the explosion. I apply the analysis to SN2014J and discuss several scenarios. For SN 2014J, the environment is likely formed by the AD wind running into a region produced by the Red Giant (RG) wind from the progenitor star prior to its WD stage. The delay times between the formation of the WD and the explosion is suggested to be short, ∼ 10⁵ yr. Finally the same analysis is repeated with other wellobserved SN, including SN2001fe, PTF 11kx, SN2006X, and SN2007le.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Dragulin_fsu_0071E_12745
 Format
 Thesis