Novel Immersed Interface Method for Solving the Incompressible Navier-Stokes Equations

Persistent Link:
http://hdl.handle.net/10150/202770
Title:
Novel Immersed Interface Method for Solving the Incompressible Navier-Stokes Equations
Author:
Brehm, Christoph
Issue Date:
2011
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
For simulations of highly complex geometries, frequently encountered in many fields of science and engineering, the process of generating a high-quality, body-fitted grid is very complicated and time-intensive. Thus, one of the principal goals of contemporary CFD is the development of numerical algorithms, which are able to deliver computationally efficient, and highly accurate solutions for a wide range of applications involving multi-physics problems, e.g. Fluid Structure Interaction (FSI). Immersed interface/boundary methods provide considerable advantages over conventional approaches, especially for flow problems containing moving boundaries.In the present work, a novel, robust, highly-accurate, Immersed Interface Method (IIM) is developed, which is based on a local Taylor-series expansion at irregular grid points enforcing numerical stability through a local stability condition. Various immersed methods have been developed in the past; however, these methods only considered the order of the local truncation error. The numerical stability of these schemes was demonstrated (in a global sense) by considering a number of different test-problems. None of these schemes used a concrete local stability condition to derive the irregular stencil coefficients. This work will demonstrate that the local stability constraint is valid as long as the DFL-number does not reach a limiting value. The IIM integrated into a newly developed Incompressible Navier-Stokes (INS) solver is used herein to simulate fully coupled FSI problems. The extension of the novel IIM to a higher-order method, the compressible Navier-Stokes equations and the Maxwell's equations demonstrate the great potential of the novel IIM.In the second part of this dissertation, the newly developed INS solver is employed to study the flow of a stalled airfoil and steady/unsteady stenotic flows. In this context, a new biglobal stability analysis approach based on solving an Initial Value Problem (IVP), instead of the traditionally used EigenValue Problem (EVP), is presented. It is demonstrated that this approach based on an IVP is computationally less expensive compared to EVP approaches while still capturing the relevant physics.
Type:
text; Electronic Dissertation
Keywords:
Floquet; immersed; moving boundary; Navier-Stokes Equations; Aerospace Engineering; biglobal; blood flow
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Aerospace Engineering
Degree Grantor:
University of Arizona
Advisor:
Fasel, Hermann F.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNovel Immersed Interface Method for Solving the Incompressible Navier-Stokes Equationsen_US
dc.creatorBrehm, Christophen_US
dc.contributor.authorBrehm, Christophen_US
dc.date.issued2011-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractFor simulations of highly complex geometries, frequently encountered in many fields of science and engineering, the process of generating a high-quality, body-fitted grid is very complicated and time-intensive. Thus, one of the principal goals of contemporary CFD is the development of numerical algorithms, which are able to deliver computationally efficient, and highly accurate solutions for a wide range of applications involving multi-physics problems, e.g. Fluid Structure Interaction (FSI). Immersed interface/boundary methods provide considerable advantages over conventional approaches, especially for flow problems containing moving boundaries.In the present work, a novel, robust, highly-accurate, Immersed Interface Method (IIM) is developed, which is based on a local Taylor-series expansion at irregular grid points enforcing numerical stability through a local stability condition. Various immersed methods have been developed in the past; however, these methods only considered the order of the local truncation error. The numerical stability of these schemes was demonstrated (in a global sense) by considering a number of different test-problems. None of these schemes used a concrete local stability condition to derive the irregular stencil coefficients. This work will demonstrate that the local stability constraint is valid as long as the DFL-number does not reach a limiting value. The IIM integrated into a newly developed Incompressible Navier-Stokes (INS) solver is used herein to simulate fully coupled FSI problems. The extension of the novel IIM to a higher-order method, the compressible Navier-Stokes equations and the Maxwell's equations demonstrate the great potential of the novel IIM.In the second part of this dissertation, the newly developed INS solver is employed to study the flow of a stalled airfoil and steady/unsteady stenotic flows. In this context, a new biglobal stability analysis approach based on solving an Initial Value Problem (IVP), instead of the traditionally used EigenValue Problem (EVP), is presented. It is demonstrated that this approach based on an IVP is computationally less expensive compared to EVP approaches while still capturing the relevant physics.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectFloqueten_US
dc.subjectimmerseden_US
dc.subjectmoving boundaryen_US
dc.subjectNavier-Stokes Equationsen_US
dc.subjectAerospace Engineeringen_US
dc.subjectbiglobalen_US
dc.subjectblood flowen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineAerospace Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFasel, Hermann F.en_US
dc.contributor.committeememberBrio, Moyseten_US
dc.contributor.committeememberKerschen, Edward J.en_US
dc.contributor.committeememberTumin, Anatolien_US
dc.contributor.committeememberFasel, Hermann F.en_US
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