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

2011 2011

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Abstract (summary)

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.

Indexing (details)

Applied Mathematics;
Mechanical engineering;
Computer science
0364: Applied Mathematics
0548: Mechanical engineering
0984: Computer science
Identifier / keyword
Applied sciences; Blood flow; Floquet; Immersed Interface; Moving boundary; Navier-stokes equations
Novel Immersed Interface Method for Solving the Incompressible Navier-Stokes Equations
Brehm, Christoph
Number of pages
Publication year
Degree date
School code
DAI-B 72/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Fasel, Hermann F.
Committee member
Brio, Moyset; Kerschen, Edward J.; Tumin, Anatoli
The University of Arizona
Aerospace Engineering
University location
United States -- Arizona
Source type
Dissertations & Theses
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
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