東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Development of a High-Order Cut-Cell...

Kaur, Sharanjeet.

Linked to FindBook

Google Book

Amazon

博客來

Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization./
Author:	Kaur, Sharanjeet.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	123 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
Subject:	Aerospace engineering. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30571659
ISBN:	9798380411370

Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization.
Kaur, Sharanjeet.

Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 123 p.

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2023.

This item must not be sold to any third party vendors.

Computational fluid dynamics (CFD)-based aerodynamic design optimization requires automation, particularly when dealing with complex geometries that require boundary conforming meshes. To address this issue and help automate the design optimization process, non-boundary conforming meshes can be used, leading to cut-cell methods. However, cut-cell methods introduce their own challenges, one of which is a potentially ill-conditioned discretization due to some cut-cells being orders of magnitude smaller than regular shaped cells. Various techniques have been developed to tackle this issue, most of which require special treatment for dealing with small cut-cells. This thesis introduces a cut-cell method based on the discontinuous Galerkin difference discretization (cut-DGD) that does not require any special treatment of cut-cells to eliminate ill-conditioning. The first part of this thesis presents the cut-DGD discretization method, which uses an underlying discontinuous Galerkin (DG) discretization. The role of DGD basis functions and the stencil construction in maintaining a well-conditioned cut-DGD discretization is discussed, and numerical experiments are conducted to show that the condition numbers of the cut-DGD mass and stiffness matrices remain bounded as the size of the cut cell approaches zero. Furthermore, the accuracy of the cut-DGD discretization in solving the one-dimensional steady-state linear advection equation and the two-dimensional Poisson partial differential equation (PDE) is demonstrated in the presence of small cut-cells. The second part of the thesis focuses on performing numerical integration of arbitrarily shaped cut-cells. A level-set formulation is developed to approximate the geometries of general shapes, such as airfoils, which are of interest in aerodynamic applications. The impact of increasing the number of boundary points and applying high-order corrections to improve the accuracy of the level-set approximation is discussed. The level-set definition of a given geometry is necessary to apply the quadrature algorithms used in this work. Two different quadrature algorithms are explored: one that requires user-defined bounds on the level-set function, which can be challenging for geometries with discontinuities (e.g., trailing edges of airfoils), and another that only requires polynomial-type level-set functions without such bounds. Fluid-flow accuracy studies are conducted to demonstrate the high-order accuracy of cut-DGD, using both exact and approximate level-set functions, by solving two-dimensional Euler equations.The final part of the thesis presents contributions towards gradient-based design optimization. Specifically, the sensitivity analysis of cut-DGD is derived, and the semi-automatic differentiation of a cut-cell quadrature algorithm is performed. These derivatives are then verified against a finite-difference approximation. A discrete adjoint approach is used to perform sensitivity analysis and to compute adjoint variables necessary for solving functional sensitivity derivatives, which are further required for a gradient-based optimization algorithm. The residual sensitivity derivative is verified against finite-difference approximations for a model flow problem.

ISBN: 9798380411370Subjects--Topical Terms:

1002622
Aerospace engineering.
Subjects--Index Terms:

Computational fluid dynamics

Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization.
LDR:04495nmm a2200385 4500 001 2397248
005 20240617111356.5
006 m o d
007 cr#unu||||||||
008 251215s2023 ||||||||||||||||| ||eng d
020 $a 9798380411370
035 $a (MiAaPQ)AAI30571659
035 $a AAI30571659
040 $a MiAaPQ $c MiAaPQ
100 1 $a Kaur, Sharanjeet. $0 (orcid)0009-0001-6150-8321 $3 3767010
245 1 0 $a Development of a High-Order Cut-Cell Method for CFD-Based Design Optimization.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 123 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
500 $a Advisor: Hicken, Jason E.
502 $a Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a Computational fluid dynamics (CFD)-based aerodynamic design optimization requires automation, particularly when dealing with complex geometries that require boundary conforming meshes. To address this issue and help automate the design optimization process, non-boundary conforming meshes can be used, leading to cut-cell methods. However, cut-cell methods introduce their own challenges, one of which is a potentially ill-conditioned discretization due to some cut-cells being orders of magnitude smaller than regular shaped cells. Various techniques have been developed to tackle this issue, most of which require special treatment for dealing with small cut-cells. This thesis introduces a cut-cell method based on the discontinuous Galerkin difference discretization (cut-DGD) that does not require any special treatment of cut-cells to eliminate ill-conditioning. The first part of this thesis presents the cut-DGD discretization method, which uses an underlying discontinuous Galerkin (DG) discretization. The role of DGD basis functions and the stencil construction in maintaining a well-conditioned cut-DGD discretization is discussed, and numerical experiments are conducted to show that the condition numbers of the cut-DGD mass and stiffness matrices remain bounded as the size of the cut cell approaches zero. Furthermore, the accuracy of the cut-DGD discretization in solving the one-dimensional steady-state linear advection equation and the two-dimensional Poisson partial differential equation (PDE) is demonstrated in the presence of small cut-cells. The second part of the thesis focuses on performing numerical integration of arbitrarily shaped cut-cells. A level-set formulation is developed to approximate the geometries of general shapes, such as airfoils, which are of interest in aerodynamic applications. The impact of increasing the number of boundary points and applying high-order corrections to improve the accuracy of the level-set approximation is discussed. The level-set definition of a given geometry is necessary to apply the quadrature algorithms used in this work. Two different quadrature algorithms are explored: one that requires user-defined bounds on the level-set function, which can be challenging for geometries with discontinuities (e.g., trailing edges of airfoils), and another that only requires polynomial-type level-set functions without such bounds. Fluid-flow accuracy studies are conducted to demonstrate the high-order accuracy of cut-DGD, using both exact and approximate level-set functions, by solving two-dimensional Euler equations.The final part of the thesis presents contributions towards gradient-based design optimization. Specifically, the sensitivity analysis of cut-DGD is derived, and the semi-automatic differentiation of a cut-cell quadrature algorithm is performed. These derivatives are then verified against a finite-difference approximation. A discrete adjoint approach is used to perform sensitivity analysis and to compute adjoint variables necessary for solving functional sensitivity derivatives, which are further required for a gradient-based optimization algorithm. The residual sensitivity derivative is verified against finite-difference approximations for a model flow problem.
590 $a School code: 0185.
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Computational physics. $3 3343998
650 4 $a Fluid mechanics. $3 528155
653 $a Computational fluid dynamics
653 $a Design optimization
653 $a Stencil construction
653 $a Partial differential equation
690 $a 0538
690 $a 0216
690 $a 0204
710 2 $a Rensselaer Polytechnic Institute. $b Aeronautical Engineering. $3 2093993
773 0 $t Dissertations Abstracts International $g 85-03B.
790 $a 0185
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30571659